We always park in the large general car park right by Wembley Stadium. Never had to book, just turn up early enough. Think is was about £25 the last time we went. Just make sure you get back to the car ASAP otherwise you'll be queueing for about an hour on the surrounding roads before you can get properly on your way home. Reading about the empty seats there will be, perhaps the traffic won't be so bad when it's finished.
Most of the businesses offering parking along the roads leading to the stadium look OK, although some appear to pack the cars in so you could be blocked in until others have left.
Edit - looking at the website, the car park I've always used may now not be much a car park. Most of it appears to be under construction, so perhaps no help for you, sorry.