Coming back - which line are you coming in on/where is he parking?
The way to Wembley Park will be full, and there is usually a solid mass all the way, and probably for 45 minutes or so afterwards (based on Rugby League cup finals, rather than football, admittedly). I don't know about travelling outwards, but there are two lines there, and three routes, once you arrive, so maybe not too awful once on the tube.
If you're on the Bakerloo line, the walk down after the Arsenal semifinal was fairly calm, and the station is far enough away to not get as many, a little busy at the entrance maybe, but not much more than that.
Wembley Stadium overground is madness (directly SW of the ground, and very close), huge numbers in an enclosed channel and less regular trains.