England lead World Cup Qualifying Group F and are six points ahead of fourth-placed Scotland, who lost 3-0 to the English in November.
"I think we're capable of winning 2-1," Brown told BBC Radio Scotland.
"I'm the eternal optimist. I'm genuinely confident. I share Gordon Strachan's feeling that we can win."
Brown's Scotland won 1-0 at Wembley in 1999 but it was not enough to overturn the 2-0 deficit from the first leg of their Euro 2000 play-off.
Subsequent meetings between the sides have all ended in England wins - 3-2 at Wembley in 2013, 3-1 at Celtic Park the following year and 3-0 when the sides met earlier in the current qualifying campaign.
"I always am very confident," said Brown.
"I genuinely believe that the 'Braveheart stuff' is not enough. It's a calm assurance and an authority which will win the game and I'm sure Gordon will instil that in his players.
"Shouting and putting on the war paint is not good enough to beat a quality team like England.
"When we were at Wembley recently, we created three or four really good chances. If I were Gordon, I'd be saying that's the kind of chances that we're capable of making."
And Brown believes Celtic trio Craig Gordon, Kieran Tierney and Stuart Armstrong, as well as Hull City defender Andrew Robertson, will be crucial to Scotland's chances.
"England will make chances, I'm sure of that so I think Craig Gordon could be the key player for us," said Brown.
"It's being realistic. They're going to make a chance or two and Craig Gordon is an outstanding goalkeeper but at the other end of the pitch, Armstrong running in behind will cause them a problem.
"If we've got the two young full-backs playing, I think they're the best young full-backs around and I'm quite sure Tierney and Robertson can damage England down the flanks."
Craig Brown, the last Scotland manager to lead the side to victory over England, is "very confident" the Scots can win on Saturday evening.