I'm not so sure. Unless you're interested in football, you would have no idea or interest in where a football ground is, particularly if you're not from round there. I'm hugely uninterested in football, I've lived in Birmingham, Stafford, and The Hague, they've all got football teams, and I have not got a clue where any of their grounds are. Also, if you're trying to dump a car furtively, why would you head towards a place where you know your regulars go? Might you not be increasing the risk that you are recognised? And, if this was James Galway man, the fact he then hailed a cab for such a short ride suggests he was a bit lost - if he did not know how to get back from the football ground, would he have known how to get to it?
Looking at the map, I would say that from the PoW (if we suppose that's where her car was) the driver, after he crossed the river, simply stayed on the same road. This then bends around to the left, so once he's about a mile and a half from the PoW, he's looking to dump the car and get back. He doesn't turn right across the traffic because it's easier just to turn left, but the first available left turn that's not a dead end is a surprisingly long way from Putney Bridge, so he takes the first he sees. Any road he turns into at this point ends at Stevenage Road. He doesn't turn left, because that's back towards Putney. So he turns right, and as he gets near the football ground, he possibly figures he should dump the car now in case this is where this road starts getting busier.
He exits the car but turns and walks back along Stevenage Road, perhaps because he saw someone on foot ahead of him, who could possibly identify him later were he to walk on and walk past.
The question with all these claims is when they surfaced, i.e. in 1986 or whether they only emerged after the police named him. The one about his prison nickname being Kipper is a classic example of this. Joshing lags called him that after the media and the plod said he was Mr Kipper, so its evidentiary value is nil. Likewise, the supposed sightings in 2000 of a woman and a man arguing in a black BMW are obviously completely unreliable. Nobody can remember the time and date of something that happened fourteen years before, and anyway, Cannan did not have a black BMW in 1986. The amount and nature of the unlikely detail provided debunks most of this supposed evidence.