He estimated its date of manufacture as early Sixties. Mrs King said: "They're going for Sixties and Seventies. Fifties they're going mad for."
Her price was £32. And, yes, the watch started when wound. Well, would you buy a cheap secondhand watch at a market stall, "as seen" and with no guarantee?
I had first met Mr Balfour only minutes earlier at the Man in the Moon pub. Wearing a yellow scarf as identity and a tweed overcoat, he had beckoned from behind a glass of red wine in the back bar.
Mr Balfour was raised beside the Stones of Stenness in the Orkneys and has written books on Megalithic mysteries. His great-grandfather built a temperance hotel in Dundee. His grandfather was MP for Hampstead. He himself has published 300 books and dealt in antiquarian books.
I had asked him to guide me through the mysteries of the secondhand wristwatch market because he is also author of the first inexpensive guide to wristwatches: a pocket-sized Wristwatch Almanac, just published at £6.99. It lists 50 classic makers' names and prices their best-known designs.
We turned knurled knobs, pondered the aesthetics of chunkiness and "friendly faces". But I could not bear to part with even £30 for a knocked-about mechanical watch.
He surprised both Mrs King and me by paying her £38 for a pretty watch with cushion-shaped dial (square with rounded edges) - and no name. Mrs King said: "My people won't buy if there's no name." Mr Balfour said confidently: "There's bound to be a name inside."
By the following weekend when I met him again - same pub, same yellow scarf, same tweed overcoat, this time in search of Rolex on a Sunday - I had had words with auctioneers and other watch dealers. As a result, the mysteries of time, as worn on the wrist, had assumed megalithic proportions and I was clutching my tenners ever more tightly. Here are some of the I-told-you-sos I heard - guaranteed to put the wind up punters with thin wallets.
George Somlo, Britain's biggest watch dealer, Piccadilly Arcade, London: "The £30 watch is never going to work well. Even if it is still going when you get home you are going to have problems. Nothing under £1,000 is worthwhile."
And antiques of today? A new £2,000 watch could be worth as little as £500-£600 by the time you walk out of the shop, says Mr Somlo.
"I wouldn't like to guarantee today's watches in 60 years' time. They will not be around. Manufacturers cut corners".
Tina Millar, Sotheby's watch auctioneer: "It's pure fashion. I urge people to buy International Watch Company (IWC) watches, which take up to 18 months to make. But they don't."
Oliver Saunders, Bonhams auctioneer: "Rolex are hyped up. They are not value for money."
Back to the stamp collection? Not yet. To the persistent punter, such barbs are tips in disguise:
n Never buy new. Last month an 18ct gold Patek Philippe at Harrods, listed at £6,500 but reduced to half price - a seemingly indisputable bargain - attracted a paltry £900-£1,500 from a reputable London dealer offered it unseen. At auction, wristwatch prices are 30-35 per cent of the retail price.
n Whether buying at the top or bottom of the market, get to know a good, reasonably priced restorer.
n Look for names whose craftsmanship is likely to be revalued upwards in a maturing market.
And maturing it is. The fact that a £500 Gucci fashion wristwatch may not fetch even £50 secondhand indicates increasing discrimination. Flashy, expensive mechanical wristwatches were an Eighties phenomenon. The market bust in 1989. Now prices are rising again - by 10 per cent a year in the past three years, Mr Somlo estimates.
For the British, not yet feeling good enough to move house or change cars, watches have become a solace purchase. Another London dealer, David Duggan, says 25 per cent of his sales are to the British, compared with hardly any five years ago. Money once spent on "castles and cars", now goes on clothes and watches - "the same as the Italians".
As for quality names rising in an overhyped market, every trader and auctioneer has "a little list" in which well-made but under-promoted and under-valued watches such as Ms Millar's cherished IWCs are given the ranking they deserve. Mr Somlo's list rates as first class Patek Philippe, Vacheron Constantin, Audemars Piguet and pre-1960 Cartiers. Then Rolex in a category of its own. Third: Jaeger LeCoultre, Movado, IWC. Fourth: Omega, Longines. He reckons Jaeger LeCoultre, Omega and Longines of the late Twenties to Forties are undervalued: "You can't buy a good Patek Philippe for under £4,000 but you can still buy a good Jaeger LeCoultre for under £1,500."
Oliver Saunders's top names: Patek Philippe, Vacheron Constantin, Audemars Piguet, Piaget: then, one step down - Rolex, Ebel, Jaeger, IWC. He explains that while Rolex makes 200,000 watches a year, Patek Philippe makes only 10,000-15,000 - "closest to hand-made you can get".
Movado, a secret favourite of Mr Balfour and many dealers, is also tipped as undervalued by John Das. He has a stall, the Oyster Bar, in Camden's Sunday market where he specialises in Rolex, putting his trust in the company's astute extraction of endorsements from famous explorers and sportsmen. Mr Das's investment predictions for the Rolex Bubbleback: the 9ct gold model, £1,500-£1,600 three years ago, is approaching £2,000 and will be more than £2,300 in three years' time. The 18ct model was £2,200-£2,300 three years ago, has now topped £4,000 and could be at least £4,500 in three years' time - "but I wouldn't sell it here; I'd take it to Sotheby's. I've got a good name, but in a market people feel trepidation parting with anything over £700."
With a sharp blade, he prised open Mr Balfour's £38 cushion-shaped watch. "A fairly good movement," he said. By that time the watch was known to be gaining seven minutes a day.
"That means you must have the hair-spring cleaned," said Mr Das, prodding a time-keeping lever with tweezers, "when it's greasy it swings too quickly." And there, discernible only with an eye-glass, a name: Mudina. Not one in Mr Balfour's book.
"Never mind," said Mr Das, "you wanted it, you bought it. I buy watches all the time that people go Huh! at."
I recalled the different world of Mr Somlo. The Rolex Princes he sold for £250 each 10 years ago he now sells for £8,000-£10,000. Mr Das will not touch them: they are out of his league.
Mr Somlo said: "We did try to get involved in the inexpensive market but a £200-£300 watch can cost that much to restore and even then we might not be able to guarantee it. We do like everything to be in pristine condition." A watch, he said, should be serviced every couple of years, "or you might as well throw it away".
I did eventually penetrate the workings of the cheap watch trade. Ian Franklin, managing director of the leading dealer-repairers CR Frost, in Clerkenwell Road, centre of the London watch trade, showed me a series of cheap wristwatches supplied by fellow traders. A Fifties Accurist with rolled gold case and 21 jewels had cost £15 over the counter, would cost £10-12 to clean and overhaul and sell for £45 with a three-month guarantee.
Only £10-£12 for cleaning/ overhaul? Ah, that is the trade restorer's price to dealers who give them bagfuls of a couple of dozen watches. If you intend collecting you will accumulate your bagful soon enough. If you have only one much-loved watch to clean and overhaul and you live in London, go straight to a Clerkenwell repairer. A high street jeweller will send your watch to Clerkenwell Road and charge you twice the price he pays. A reasonable price for a complications-free clean and overhaul is £25-£30.
Mr Franklin buys watches at house sales and other non-specialist auctions. Big dealers pack Christie's and Sotheby's watch auctions - keeping prices low rather than competing among themselves. There will probably be 1,500 bargain seekers at the Midland Clock and Watch Fair, the country's biggest, at Solihull tomorrow (see below). Average price is less than £50 and most pieces await restoration.
`The Wristwatch Almanac' by Michael Balfour, £8.50 inc p&p from Eric Dobby Publishing, 12 Warnford Road, Orpington, Kent BR6 6LW.