He was eight years old, had been in the city all his life and was watching a brand new team take on Gainsborough Trinity. Posh won 4-0, he recollects, with a grin. Eric had loved football before that match, but this win solidified it: he'd be cheering for Posh from that day forward.
Not just cheering, in fact. Eric played for Posh reserves, with a number 10 on his shirt. He had one outing for the first team - in the Maunsell Cup against Rushden in 1947, he says, although his story doesn't end with a win. He didn't even get to keep his shirt - "they cost too much in those days, we weren't allowed to take them away!"
Football wasn't officially taught at school, but plenty of Belsize Avenue boys took to the pitch. Some even went on to make it big - "Des Farrow, he went on to play for QPR; Johnny King went to Leicester; Derek Woolley found himself at West Bromwich Albion" - but despite a few call-ups (he was asked to trial at Wolves during the Second World War) Eric stuck to the amateur game.
Which was more exciting than the first impression suggests. Eric was posted to Africa in 1948 as part of his national service, staying for 20 months, and has fond memories of playing the beautiful game in Ghana.
Accounting was Eric's day job, but he says it's football and his family that have kept him young at heart. His wife of 59 years, Vivian, sadly passed away last year, but he sees his sons Garry and Stuart and his daughter Karen as often as he can, as well as his four grandchildren. Sometimes they accompany him to London Road, where's he's been honoured as one of the club's most long-standing supporters.
What does he think of the plans to move the stadium? He's uncertain: "Like all changes, it won't be the same anywhere else. But things do change. I remember being at the stadium when the Glebe Road side was all sleepers."
Eric also remembers the days where the players didn't need to be quite so fit as they are now. There are more tackles, less space - and, of course, a fair bit of diving. He shakes his head at the thought - but there's a twinkle in his eye when he says that some of the players of old weren't unfamiliar with a dive or two to get a decision to go their way. Did he mention any names? We'll never tell.
In 87 years of watching Peterborough United, there are plenty of games and players that hold a special place in Eric Heath's heart - but he's got two that prompt almost perfect recall.
The first, he says, is a January 1957 FA Cup replay away against Lincoln City - one of Posh's fiercest rivals, "though not as fierce as Northampton or Kettering". Peterborough won, though with a 5-4 scoreline it wasn't a given, and then went on to play Huddersfield in the next round. "We lost that one," said Eric, matter-of-fact, but not disheartened.
The second is a game played in a blizzard. It's the FA Cup third round in 1960, Peterborough are away at Ipswich Town and, as per Eric's memory, "all you could see was snow". The score was tied at 2-2 with five minutes to go, the weather was terrible, but Posh had a corner. And Dennis Emery, Eric's favourite player, was waiting to grab that winner.
It's no surprise, then, that Emery makes Eric's dream starting 11. Or, erm, starting 13, because we decided we needed substitutes and Eric couldn't decide who to cut.
David Seaman takes the goalkeeper's spot, followed by a back four of Andy Edwards, Chris Turner, Ted Chiverton and Adam Drury. Next, is Bob Doyle, Mick Gooding, Billy Hails and Ipswich Town's nightmare Dennis Emery. Leading the attack is Derek Dougan, Terry Bly, Tommy Robson and Peter McNamee.
None of the current guys, but Eric likes what he sees in Posh right now, even if they did "keep us hanging on" with the slight delay to promotion celebrations. He's appreciative of the recruitment - and who wouldn't be with Jonson Clarke-Harris succeeding Ivan Toney, both league topscorers - and sees Peterborough United as a unit that's working together.
"It's not just about whether the manager's doing a good job," he says, although he thinks Darren Ferguson is. "It's the players and the support team wanting to work for it too."
Eric has spent the past year listening to Posh commentary on the radio, which he enjoys doing, but he's hopeful of getting back to a match next season. And he reckons the club will be fine in the Championship. "Depends who they sell," he quips, though he's satisfied with all the contract renewals so far.
After a year without fans - from those who have been there from the very start, like Eric, to those who might not even have got to a game yet - filling that ground should give Posh a lift, too.