Brown was the last man to lead the Scots to a summer finals when his squad qualified for the 1998 World Cup in France. A year later, however, there was anguish as the team lost out in a two-legged play-off against England as they were denied a place at Euro 2000.
A 2-0 defeat at Hampden did the damage as Kevin Keegan's side won through to Holland and Belgium but there was the consolation of a single-goal victory in the Wembley return as Don Hutchison netted his famous header.
Brown would love to see Strachan eclipse his feat of winning in London when the sides meet on Wednesday but insists steering the Scots to Euro 2016 in France is far more important to his long-term reputation.
He told Press Association Sport: "Gordon is already a legend in Scottish football and a win would help that. But he doesn't need to beat England to cement his legacy.
"I think it's more important that we qualify for the European Championships next time than it is to win at Wembley. But a win against the Auld Enemy would be a bonus."
Strachan was drafted in to pick up the pieces following a disastrous start to World Cup qualifying but could not revive the desperate situation left for him by former boss Craig Levein as defeats to Wales and Serbia cost Scotland their place in Brazil next summer.
But the recent 1-0 win over Croatia in Zagreb has raised hopes that the side may have finally turned the corner.
And Brown - who also managed the Scots for their Euro 96 clash with England - has no doubt the new manager will field a side more than capable of holding their own against their more sizeable neighbours.
"I never felt pressure at any time during my time as manager of Scotland and neither should Gordon," he said. "I always worked to the philosophy that if you do your utmost, then that was all you could do. I was fiercely determined and competitive but I didn't lose any sleep.
"People asked me after we lost here 2-0 to the English in 1999 if I feared we were going to be humiliated in London. But I never felt that way. I was always optimistic because I had faith in my team.
"I still feel the same with this group and as a fan, I'm optimistic. I'm desperate for us to win the game on Wednesday. It will be very tight. In the last 10 games against England, neither side has scored more than two goals. It will be a mistake, a poor decision or maybe a penalty that decides it.
"The only piece of brilliance I can remember in this game was Paul Gascoigne's goal at Euro 96. But I don't think you will see that this time. I think it will be dour. There will be one goal in it. But we shouldn't fear a complete doing. It won't be another 9-3."
Around 20,000 members of the Tartan Army will descend on the English capital for Wednesday's match and Brown expects them to have an impact on the result, even through the game is a mere "friendly".
He said: "A friendly between Scotland and England is the equivalent of a competitive match between any two other counties in the world. I was involved in seven games with England - four in the Rous Cup as an assistant and three as a manager. They were all competitive and we never had a friendly with them.
"And I'm sure this won't be played like a friendly either. Certainly not from a Scottish perspective. We are out to continue the progress from that fine win in Croatia and, you know, it is the Auld Enemy we are facing.
"We don't talk about playing England, we talk about playing THEM. So it's important to us. Certainly more to us than to the English. And it will mean more to our supporters. They might have more numbers supporting England but they won't match us in volume."
- Sports & Recreation