With Bradford City, he came within a goal-line clearance of knocking out a Tottenham Hotspur side featuring Jimmy Greaves, Alan Mullery et al in the third round.
Counter-balancing that high of 1970 when Spurs were relieved to leave Valley Parade with a replay was Ham twice coming within a whisker of being humbled by non-League opposition in the Cup when sporting the colours of Rotherham United and Bradford Park Avenue.
Such contrasting experiences mean Ham, now 71 and for the last five years a director of FC Halifax Town, will travel to Milton Keynes today for the re-formed Yorkshire club’s tie in excited mood.
“I love the FA Cup,” said Ham when speaking to the Yorkshire Post ahead of the Shaymen’s second appearance in the first round proper since being formed out of the ashes of the old Halifax Town.
“It is still a fantastic competition, I don’t care what anyone says. And particularly so for the smaller clubs, whom it brings nothing but good to.
“For us, drawing Charlton Athletic at home a couple of years ago was massive. We don’t have an Abramovich or anyone like that to fund the club.
“So, the sort of income we got from being shown live on television and the gate receipts (from an attendance of 4,601, who saw Charlton prevail 4-0) really helped the club.
“It allowed us to put some money into the squad and also put some away for a rainy day, which is how we are determined to run the club.
“The Cup has that potential for a fairytale result and, obviously, that is what we would love to have at MK Dons.”
It will not be easy for Neil Aspin’s side to create their own slice of Cup folklore. Fifty-three places separate the two clubs in the football pyramid but, in reality, the two are light years apart.
While the Dons have for the past decade been bankrolled by Peter Winkelman, Halifax remain part-time even though three promotions in four years have brought a return to the Conference.
In a division where a host of former Football League names throw money around in the hope of winning a return, the Shaymen have overcome this considerable handicap to make a pleasing start. They will travel to stadium:mk today sitting 12th.
However, despite such an impressive performance back in the fifth tier, Halifax are very much ranked as outsiders today as the focus turns to the world’s oldest knockout competition.
Ham said: “To have 25 points by the start of November – which is halfway towards the points total that is usually enough to stay up – has to be pleasing, especially when you consider we are part-time.
“We are one of the minnows in this league but we have equipped ourselves well. We have a young side and Neil is holding things together well. We have been struggling a bit away from home but Neil is working on that.”
As for today’s meeting with League One opposition, Ham added: “I have been to the new stadium at Milton Keynes and it is a fantastic arena.
“I actually know the MK Dons chairman really well. We got to know each other when I was involved at Bradford and they played against Milton Keynes.
“He always made us feel very welcome, and me and him built up a good rapport. Obviously, I only see him from time to time but when we do meet we are like two long-time friends. He is really passionate about his football.”
Ham, of course, enjoyed a 15-year career as a professional footballer playing for a host of clubs, including two spells with both Park Avenue and City.
During that time, he enjoyed a fair share of Cup ties so knows that even the odds being against Halifax today does not mean that a home win is guaranteed.
“My favourite Cup memory as a player came when Bradford drew 2-2 with Spurs at Valley Parade,” he recalls. “We went 2-0 down early on (to goals from Greaves and Roger Morgan) and, obviously, you fear the worst against a team as good as Spurs were back then.
“They were one of the best teams in the country at the time with the likes of Jimmy Greaves, Cyril Knowles, Mike England and so on.
“But we fought back and could have won it. Cyril Knowles blocked a John Hall shot on the line with about 20 minutes to go. If that had gone in, we could have won it.
“Valley Parade was heaving with more than 20,000 in the ground and the crowd really got behind us. We were so close to going through but then lost the replay 5-0.”
Ham added: “I also experienced the other side of football in the FA Cup. I remember playing for Bradford Park Avenue against Witton Albion one year. We were in the old Fourth Division, while they were two or three leagues below us.
“But that didn’t stop them going 2-0 up. With about 20 minutes to go, it was still 2-0 but then, thankfully, we sorted ourselves out and ended up winning the tie in the last minute.
“There was another time when I was at Rotherham. We were losing 1-0 to Frickley in the Cup and it took a ‘94th-minute’ equaliser to earn a replay, which we won something like 5-0.
“But we were so close to going out and that is the Cup. Hopefully, we can spring a shock this year.”