As suggested….I'd try & park at one of the outer train stations & get the tube in. Watford Junction (not tube) to Wembley Central is pretty good, but I know they are doing lots of work at Wembley Central at the moment (to the station & surrounding area) so check for disruption (I'm originally from Wembley).
Wembley Central to the Stadium is about a 20 min walk, either go:
all the way up the high st (right out of station) all the way to the 'triangle' junction with a crappy clock in the middle of the road then turn left.
or, right out of the station, then left at the junction opposite 'The Bear' pub (I think it's called). Keep going straight to a set of lights. Straight over there & you'll end up at Wembley Park station (it's a more residential walk with no pubs/food choices), right at the top of the pedestrian bit you see on the TV leading to the Stadium.
OR get to Amersham or Uxbridge & get the tube on the Met line to Wembley Park – the Stadium is just over the road. Last time I was down that way, there was weekend work on the branch that goes to Amersham on the Met line, so best to check that.
The only other thing I can think of, is giving a pub called The Green Man a ring. It's on Dagmar Avenue in Wembley & they used to do 'event day' parking. You could call in advance and see if they will reserve you a space. It's a decent pub only 10 mins walk from the Stadium. Not sure if they'll go for it, but worth a ring. Only problem might be traffic getting back out again.
If you haven't arranged parking in advance – don't bother driving. It will give you major stress!!