As it is, Redknapp might be forgiven a touch of wistful envy: although he ended up with 17 caps, his own career in England's midfield was notable mainly for epic misfortune. "I was carried off three times for England," he says.
"That's got to be a record. I tore my hamstring against Switzerland, and broke my ankle against Scotland and South Africa. Partly because of that I was always so tense that I didn't perform. Unless you're Wayne Rooney or Michael Owen, I think you need 15 or 20 games until you feel part of the England set-up. Frank's played 25 games or whatever; he knows that if he has the odd bad game for Chelsea, he's still going to play."
Redknapp admits that the Frank Lampard who made his name at West Ham under the guidance of their respective fathers, brothers-in-law Harry Redknapp and Frank Lampard Snr, did not seem likely to reach the summit as a footballer.
"He was always a good player, don't get me wrong, but if someone had said he was going to be one of the best players in the world, I'd have doubted it. But Frank's got incredible self-belief, more than anyone I've ever met. We're very close, we speak all the time, and although Frank might tell it different I'd say it really helps that he's settled down, with a girlfriend and a baby.
"Also, he went to Chelsea at a good time. Things weren't great to start with. There were some strong characters there - Wisey [Dennis Wise], Poyet, Petrescu; that little firm that was there - but they left and all of a sudden Frank realised that he could be top man, him and John Terry. As far as England is concerned, Euro 2004 was a big time for Frank. He wasn't one of the favourites to play, but he scored a couple of goals in the build-ups, then he started against France, scored a great header, and after that it was, 'Who plays with Frank?'"
Steven Gerrard, in Redknapp's estimation, most definitely should. "People say they can't play together, but great players work it out in the end. And David Beckham's still got a lot to offer. I'd always use him on the right, he's the best crosser of a ball in the world. Shaun Wright-Phillips is an option, but that's all he is, an option."
On the subject of the England captain, it occurs to me that the Beckhams perhaps take some of the heat, not to mention Heat, away from Redknapp and his wife, Louise, formerly a member of the group Eternal. Is he grateful to them, I wonder, for being a much higher-profile footballer/pop star couple?
"Well, Louise and I have never courted publicity, whereas David and Victoria set out to gain as much publicity as possible. But it wasn't good for his football. He needs to be a footballer rather than a celebrity, and I think he's got his head down now, which is why he's been playing well for Real Madrid. From what I'm seeing, he's running games."
Redknapp's faith in the England players does not, unsurprisingly, extend to the manager. His father is one of the regime's more outspoken critics and I suspect that the pair of them have spent many a happy hour questioning Eriksson's modus operandi, although perhaps without quite so much Latin. "I'm not trying to jump on the bandwagon, but I've never understood what Sven does. I speak to people about England training sessions, and he doesn't do a lot of coaching. Now, I can understand that after Kevin Keegan they wanted a quiet manager, someone who was a real tactician, who could change games, not a shouter and a bawler.
"That's fine. Except that every time he's needed to make big tactical decisions, he hasn't been able. Playing five in midfield against Northern Ireland was ridiculous. He doesn't deserve the players he's got. In fact, I don't think he knows what he's got. I'd like to see Sam Allardyce in that job, or Alan Curbishley." Or Harry Redknapp? "He could do a better job than Sven, that's for sure."
It was a "terrible shame", Redknapp adds, that his last year as a footballer, spent working with his old man at Southampton, ended in relegation.
"I enjoyed that time with my dad as much as I've enjoyed any of my football. We've always got on well, but it brought us closer together. We spent so much time talking about the game. It was hard for him tactically, because he only took over at Christmas. He wanted to buy a guy from Tottenham, a defender, Paramot, but the money wasn't quite there. That could have made the difference.
"We agreed that maybe if he'd gone that way instead of getting another player, whose name I won't mention, we might have stayed up.
"But it was just great to be talking about football with him, and I learnt a lot. How he deals with situations, how he deals with people. I think man-management's the majority of the game now. Sometimes you've got to change tactics, but players have to like you, or at least, really want to play for you.
"Peter Crouch probably wasn't worth £200,000 until dad went to Southampton. He put his arm round him, told him he was a great player, that he was the man who could keep us up, and he scored 15 goals from Christmas. I said then he should play for England. I'm not saying he should start, but with 20 minutes to go ... the worst thing to do is to keep slaughtering him. I know the boy, and I like him. But you'll get nothing from him that way, whether for Liverpool or England. His confidence will go."
Not all managers, Redknapp adds, grasp the fact that different players have different needs. "Dad does. He was great with me. I couldn't train every day, and he understood that, not because I was his son, but because he wanted me in the team. At Liverpool when I was struggling with my knee, Gérard Houllier tried to make me train twice a day. You have to know your players.
"But then dad was a player himself; Gérard never had that experience. If you ask me to train twice a day, I'm going to break down. There's a lad at Southampton, Svensson, who's got a similar knee injury to mine. Dad's great with him. He says to him: 'If it's not right, have a day off ... go on the bike.'"
I bring up his father's reputation as one of football's most irrepressible wheeler-dealers, a bit of a Del Boy, which is a subject that troubles him. But at the same time he must know where it comes from. I tell him that Harry once gave me a lift from his home to Bournemouth station, and talked all the way - enthrallingly but regrettably off the record - about strokes he had pulled that could only be described as wheeler-dealing.
"Yeah, but then he's not had a lot of choice. He's never been at Arsenal or Manchester United with a lot of money to spend, and some would say that he wouldn't enjoy that. He likes putting the jigsaw together, finding someone for the left-hand side who can open it up, a Berkovic or Di Canio, a player who can solve a problem for him. He's great at that.
"And Sam Allardyce is very similar, picking up players for not much money, getting someone like Okocha to play for him. But just because dad's like that as a manager doesn't make him that way as a person. He's got a lot of class; he likes nice cars, he dresses well. I got upset recently because a journalist wrote something derogatory about him. He said you wouldn't buy a Rolex watch from him."
Redknapp's indignation hangs in the air, positively inviting my next question. "So you would buy a Rolex watch from him?"
"Oh yeah. But he'd give it me. He's incredibly generous."
So, I can testify, is Redknapp Jnr, encouraging me to help myself to the fruit and nut assortment that he has brought to a corner table in the Sky canteen. He was wooed by Sky last summer just as he was about to consummate his relationship with the BBC, which caused no little embarrassment at White City, especially as Match of the Day promos featuring Redknapp were still being aired even once he had signed for Sky.
Yet there was no bitterness, he insists. "The BBC were great with me, and it was a tough decision, but doing live games really appealed. You get there on a Sunday, there's a nice build-up, you speak about the game, turn around and there it is in front of you. I was more comfortable with that than sitting in a studio all day Saturday looking through edits."
For Sky's part, it is helpful not only to have a pretty face but also someone who was playing in the Premiership only last season. This was evident when Redknapp, before a match involving Manchester United, begged to differ with his fellow undit Ray Wilkins, who had dismissed Cristiano Ronaldo as a one-trick pony. Actually, said Redknapp, to have Ronaldo running full tilt at you, especially now that he had got a bit beefier, was pretty intimidating.
The old man, meanwhile, reckons he should go into management. "He says I understand the game. I certainly love watching it. I suppose someone would give me a job on the back of who my dad is, but I haven't done my coaching badges yet. I will do, as much for Sky's benefit as my own, because it helps to see the game as a coach as well as a player.
"I know I've still got plenty to learn. I watch Andy Gray at work, for instance, and I think that it's almost a shame he didn't become a manager.
"He sees things so quick. One of the first games I did was Middlesbrough v Charlton, which Charlton won 3-0. They scored a goal where Danny Murphy hit a great ball to Rommedahl who's made a run from the right and hit it with his left foot.
"Andy looks at this and says, "There's something not quite right there. Where's Boateng? Get me a camera angle.' This is while the game's going on. And when we get the wider picture, we can see Boateng off the field getting treatment. I thought, 'Blimey, you've got to look at everything'.
"So I want to get better at this first. Besides, I'm really enjoying my life at the moment, not having to worry about my knee. Maybe management will be there if I want to be. It definitely appeals, but it's hard work, and it affects the whole family. The first result I look for every Saturday is Southampton ... and that's because I know the impact it will have on my mum."
With this, we leave the canteen, and as we go I clock a tableful of young women eyeing him. I wonder whether to tell them that he spends Saturday afternoons worrying about his mum. That might finish them off.Reuse content