Still four months short of his 20th birthday, Clarke had left the family home in Short Heath to start a new life in London, after being signed by Fulham for £37,500 from Walsall.
“I remember my first day, a Friday,” he says. “I walked out in the corner of the ground and there he was.
“When I was growing up England matches were on Wednesday afternoons and I used to pretend to be unwell so I could stay at home and watch.
“Johnny Haynes was a regular in the team. Now here I am playing with him.
“He called over to me and said: ‘Clarke, I’m going to take three corner kicks, you tell me which part of the goal you want me to hit’.
“I think ‘go on then’ and the first one I say: ‘Near post.’
“He takes a few steps back, runs up, bit of curl on it and BANG,” says Clarke, clapping his hands together as he says the final word of the sentence for added effect.
“That’s impressive. Second one, I say ‘crossbar’ and BANG. Two out of two.
“Now it’s the last one and I say ‘near post again’. BANG. Incredible. Just incredible. What a player.”
The memory is among thousands which remain rooted in the mind of a man fascinated by footballers from an early age and who never wanted to be anything else.
“I’m the little boy whose dream came true,” adds Clarke, whose illustrious career saw him become a key component of one of English football’s most famous teams at Leeds United.
Now aged 72, it is fair to say the admiration he holds for his contemporaries is not reserved for many stars of the modern game.
“I find a lot of football nowadays quite boring, I think the money has ruined it,” he says. “In my day it was a more level playing field. Look at Manchester City. They are the best team because they have spent the most money.
“But I’ll tell you this, for all those millions they have had to pay to get those players at Man City, plus all those millions they have to pay them, that great Leeds side I was part of would bury them alive. We were better players.”
He explains: “It’s all about touch and control. In our day, we stopped the ball dead. Our team at Leeds was a league team but we were all internationals.”
Clarke will always be most closely associated with Leeds, the club where he scored 151 goals and won the league, FA Cup and Fairs Cup.
But he is very much a product of the Black Country and remains proud of his roots. After all, it was here his talent was first nurtured, on the council pitches of New Invention.
One of five brothers to play professionally, Clarke was an Albion fan growing up in the 1950s, yet it was actually Molineux where he spent most of his Saturday afternoons.
“It was three bus rides to The Hawthorns from where we lived. But just one to Wolverhampton,” he explains. “To be fair, Wolves were the best team of the decade. I watched some great players.
“Bert Williams, Billy Wright, Jimmy Mullen, Peter Broadbent, little Johnny Hancocks – I reckon he had a shot as hard as Peter Lorimer.
“I used to go behind the goal, in the North Bank and I would watch the strikers for both teams. Then I would catch the bus back home to Short Heath and would be straight out on the council football pitch, practicing what I had seen. My mom could watch us from the kitchen window. We lived and breathed on there.”
Those familiar with the image of Clarke as the tall, slender striker might be surprised to learn that for much of his childhood he was among the shortest in his class.
“When I left school at 15 I was four foot five,” he says. “I’d play for South Staffs boys, bang in three or four goals and the newspaper reports would refer to me as Tiny Clarke.
“I remember my dad telling me that when I left school, I would start growing. And I did.
“When I was a trainee at Walsall I would go to bed at 8pm every night. When you are growing that quickly it saps your strength. By the time I was 19, I was six foot.”
Growing pains didn’t denigrate Clarke’s eye for goal. He scored 23 times in his first full season after breaking into the Saddlers first-team and had 14 before Fulham made their move in March, 1966.
“I would have loved Wolves, West Brom or Villa to come in for me. But it didn’t happen,” he says. “Fulham was good for me but the club was not ambitious enough.
“It wasn’t about money. I wanted to win a trophy. The directors there were quite happy just to stay in the First Division. Well, that wasn’t good enough for me. I wanted to go and win things.”
Clarke would eventually make it to Leeds via one season at Leicester.
Things could have turned out very differently, however, had he accepted an offer to join Manchester United when they came calling in 1968, offering Fulham a then British record £150,000.
So keen was Matt Busby to acquire Clarke’s services, he and assistant Jimmy Murphy travelled to London to meet with him.
“I was told to go up to King’s Cross. I can see them getting off the train now,” he recalls. “They pointed to a taxi, so we got in they told the driver to just go around London. So that’s what we did. With them telling me about Manchester United.”
Clarke, however, turned them down, instead choosing to join Leicester after being struck by the personality of their manager, Matt Gillies.
But Gillies resigned just six months later and in the summer of 1969, after Clarke had been voted man-of-the-match despite the Foxes losing the FA Cup final to Manchester City, Leeds boss Don Revie came calling.
“He came to my house and it was obvious he’d done his homework,” says Clarke. “Leicester were paying me £100-a-week and he asked me how much it would take to get me to Leeds.
“God’s honest truth, I asked for £10-a-week more and he wouldn’t give it to me. He said all his players were on the same wage. Who was I to disbelieve him?
“I signed a two-year deal at Leeds for the same money. Do you think any players would do that today?
“But I wanted to play for Leeds and the rest is history. It was only when I got there I realised I had been told a bare faced lie. There were players on more.
“But I didn’t go knocking on his door. I thought right, I’ll show you how good I am.
“The first season I scored 26 goals. The next I got 27. Then I asked for a big rise and got it. By then I’d earned it.”
You don’t really need to listen to Clarke’s words to sense the fearsome pride for what was achieved at Leeds, merely the tone of his voice.
Revie is never mentioned by name, always “the gaffer”.
“That’s the respect I have for the man,” says Clarke, who adds: “Every morning I wake up, I think of Billy Bremner.”
Leeds a powerhouse, though they suffered their fair share of heartbreak, finishing league runners-up in each of Clarke’s first three seasons.
There was also defeat to Bayern Munich in the 1975 European Cup final and two Wembley defeats in the FA Cup.
“If you wanted to win anything, you had to get past us,” he says. “Yes, we should have won more. But back then it was a more level playing field.”
There is a pause and a sigh, before he continues: “It was special. The fans were phenomenal. Unbelievable.
“I don’t want to sound big-headed but when you look at it now, Leeds is one of the biggest clubs on the planet.
“The gaffer, with the help of us players, put that club there. In many respects it was easy, playing with those players.”
Clarke, who was also capped 19 times by England and played in the 1970 World Cup, is not afraid to talk about his own talents.
“Your great strikers, I put myself in that category,” he says. “I was born with that gift. No manager can teach a player how to score goals. You can teach a lad how to defend. You cannot teach them how to score, that instinct. I had the gift. So did Jimmy Greaves and Denis Law.”
Clarke believes no club would have been able to afford the combined wages of Revie’s Leeds team, had they played in the modern era.
“I’m not envious of the money the players get now,” he said. “People say: ‘By Christ Alan, if you played today you would be a multi-millionaire. But I played in the best era, with and against great players. It was never about money for me.”