Taylor had been told that the painting - not seen in public since 1976 - would probably sell for around pounds 1.3m. He consulted the PFA chairman, Barry Horne, who agreed that, if they could afford it, it would make a fine addition to the union's collection of football memorabilia. "He knew the painting," says Taylor, "because we have a limited edition print in our boardroom. It is the definitive football picture." And particularly meaningful for Taylor himself, because it shows people converging on Burnden Park, erstwhile and now demolished home of his first club, Bolton Wanderers.
Taylor got into his office shortly before bidding was due to begin. He called directory enquiries, asked for Sotheby's number, and rather bizarrely found himself connected to someone in Weybridge - an inauspicious, almost slapstick start to proceedings. He tried again and got through in the nick of time. Lot 40 was about to go under the hammer, starting at pounds 500,000. "When it got over a million the woman on the phone said `there are four bidders still in, Mr Taylor.' You knew it was going to go for a big price. An atmosphere had built up a bit like before a big football match. There was a real buzz."
Taylor dropped out of the bidding twice, but at pounds 1.7m was told he could probably get it by offering another pounds 50,000. Which, with a deep breath, he did. Later he found out that his rival bidders came from America and the Middle East. So instead of being shipped out of the country, the painting has been returned to its native North-west, where eventually it will go on permanent display, courtesy of the PFA, in Salford's new Lowry museum. A round of applause, if you please.
The PFA's chief executive will forgive me for saying that he is no matchstick man himself. At 55, he is every inch the affluent ex-footballer - ruddy, balding, with modest middle-aged spread. It is said that he is paid in excess of pounds 400,000, but you won't find many footballers complaining about that. By common consent, Taylor does an excellent job of representing their interests.
He has helped to develop a non-contributory pension scheme, funded by a five per cent levy on every transfer fee, which has so far paid out over pounds 20m. He has developed educational courses for footballers who do not make the grade, or are forced to retire young, enabling them to go into recreation management, or even become physiotherapists, or podiatrists (leg and foot specialists), in the insteps of the scheme's best-known beneficiary, Norman Whiteside. The PFA had just two full-time staff when Taylor took charge in 1981. Now there are 50, including many former players, such as Jimmy Armfield, who runs the coaching department, and Des Bremner, who works in the pensions office. Taylor has been trying, too, to encourage ex-footballers to become referees, though with precious little encouragement from the Referees' Association. "Lots of cricketers become umpires," he points out. "It's just so sensible."
More contentiously, Taylor insists that he was representing his members' interests when he resigned a year ago from David Mellor's Football Task Force. "The choice of David Mellor upset a lot of people, me included, but I tried to give him the benefit of my considerable doubts. For me, the Task Force's very reason for being was to look at the increased commercialisation of the game. I was worried about clubs being under the same ownership yet in the same competitions. Would we end up like Formula One, where the No 2 driver is winning and slows up to let the No 1 go past? It's already hard enough to protect the integrity of football without that happening.
"Also, I was worried about clubs becoming public companies, saying their first priority was to shareholders rather than supporters. To me, that's sacrilegious. I worried about the TV tail wagging the football dog, about Sky trying to take over Manchester United. Because in sport, if you allow the biggest to monopolise, you haven't got a sport. The essence of sport, unlike business, is that you need to work hard to create competition, whereas in business you look to eliminate competition.
"All this was put on the back burner, though, because Mellor wanted to tackle racism. That was just populism on his part. Because we'd already been doing it. We'd worked really hard, supporting initiatives like Kick Racism Out Of Soccer. And what really annoyed me was when he started using his articles in the Evening Standard to say that footballers don't give an ounce of effort back to the community. We started a community programme in 1986, after Heysel, and it has done really well. Plus there are individuals like Bryan Robson, who has raised millions for a scanner for a hospital in Manchester. Like [Alan] Shearer. I phone up to ask if he will help children with learning difficulties, and he says `I'm really busy, but use my name, and I won pounds 10,000 last month which I'd like to give to them.' So I get sick to death of footballers being damned for not putting anything back."
Taylor pauses, but not for long. "I had a word with [then Sports Minister] Tony Banks who said he couldn't get rid of Mellor because it would look bad, though I don't see why, it's not as if the Prime Minister doesn't change the Cabinet around. But I thought OK, I'll bite my tongue. The final straw was when we weren't even asked to the launch of the Task Force report. Really, to put him in charge of a task force seriously looking at my profession. I thought it disdained it, made it like Barnum and Bailey. I hate people claiming to know about the game when they've only been in touch with it for a few minutes. Everyone is entitled to have an opinion about football, that's its strength, but the politics of it, the structure, that is serious stuff. I felt I had not worked in football all my life to hear how it should be run by David Mellor, just as I would not presume to go into the House of Commons and tell them how to run their affairs."
Throughout this eloquent harangue, Taylor's voice is calm, even, and there is a hint of a smile on his face. He must be a bugger to negotiate with.
For he is many things at the same time. Forward-thinking, yet a traditionalist and unashamedly sentimental with it. He believes that football is losing the "dream factor," by which a club like Wimbledon can rise from the League's murky depths to win the FA Cup.
"The Premier League has been one of the best sells ever," he says, "when you consider that it is still the First Division by any other name. But before the Premier League there were 60 clubs in 30 years in the First Division. And look at the spread of success in Europe. Liverpool, Everton, City, United, Villa, Forest, Arsenal, Chelsea - that is becoming more and more difficult to achieve. There are fewer and fewer giant-killing acts, and coming out of the Premier League is almost like a trapdoor into financial difficulties. The Premier League gets pounds 200m from television, leaving pounds 25-30m for the other 72 clubs, and the First Division is trying to get most of that to at least hold on to the coat tails of the Premier League. There is more money in football than ever before, but try telling that to the Lincolns of this world."
Indeed. One of the oddities of Taylor's job is that he represents players earning pounds 50,000 a week, and players earning barely a hundredth of that. The average wage in the Third Division is under pounds 20,000 a year, rising to pounds 30-35,000 for Second Division players and pounds 60-65,000 for First Division players. So how does he - and for that matter, how do they - square this with Roy Keane's pay packet?
"Well, I never minded that Trevor Francis was earning more than me when I played for Birmingham, I just wanted to reach the same level. I remember going to a meeting at Bellevue in Manchester when we were trying to get rid of the maximum wage, and a chap from Bury said `I don't know why we're arguing about pounds 20 maximum. My dad earns less than that for going down the pit.' At which an old pro, with a real broad Lancashire accent, stood up and said `I hear what you say, brother. And I have every respect for your dad's job, in fact I've done it meself. But try telling your dad to come up out of that pit on a Saturday afternoon and mark brother Stanley Matthews.'"
Taylor roars with laughter. But there is a serious point to be made. "I think it's right that the top players are beginning to recognise their own worth. Think of the boxing entrepreneurs who put on fights while ex-champions like Joe Louis were working as commissionaires on the door of Las Vegas nightclubs. That is never how it should have been. And take the Rolling Stones, or Oasis. Of course they want a share of the take, along with the concert promoters. It's the same with footballers. We don't complain in this country if a TV presenter does a deal for pounds 1m a year, or a stockbroker gets a pounds 5m bonus, so what is it with footballers? Manchester United's expenditure on players' wages is only about 25 per cent [of revenue]."
Speaking of Manchester United, Taylor was, not surprisingly, an outspoken critic of United's decision to withdraw from this season's FA Cup. "I saw their first game after the Munich air disaster, against Sheffield Wednesday, when there were no names in the programme," he recalls. "That was team which went on and reached the 1958 Cup final, which shows how much the FA Cup meant to them... so I was particularly disappointed that everything wasn't done by the FA and the Government to avoid this situation."
What would he have done? "We can all be wise after the event. Like the Irish joke I wouldn't have started from the same position. They should have sorted it out in the close season, before the fixtures were done. It's terrible that the FA Cup has been devalued, and I don't think we should ever disregard what's going on in our own back garden. But then we do that in England. We have the highest aggregate attendances in the world, the most full-time professional clubs, the most full-time professional players, the most amateur clubs, about 48,000, yet we keep looking at how they do things abroad."
For all his criticism of many aspects of football and its complicated bureaucracy, and his certainty that the league as we know it will not survive the 21st century, Taylor is essentially optimistic about the game's future. "In the 1980s the game was dead on its feet. Who would have thought then that the hooligan problem would be tackled as well as it has been, or that Afro-Carribean players would have assimilated as well as they have?"
Not that hooliganism and racism have exactly vanished, and the PFA has stepped in when apparently racist feuds have erupted between two players, like those between Ian Wright and Peter Schmeichel, or Steve Harkness and Stan Collymore. "We don't always resolve it, but at least we try," he says. He knows better than anyone that his members are imperfect, but, for the most part, defends them staunchly. "People ask why players react against crowd abuse. Well, it would help if clubs and stewards would try harder to stop vindictive and vile abuse. Players can take stick if they have missed an open goal, but it's different when people are screaming things about your wife or family." Absolutely. It is no longer the game that L S Lowry knew, which is why, of course, he wanted the painting so much.