DONT go down the M1, I gather there are bad road works around Luton.
Not sure if you have been to Wembley before but DONT try to get the car anywhere near Wembley it is a waste of time.
As mushroom says, park at one of the stations on the Metropolitan line and get the train.
After coming down the M40 it turns into the A40 just after Uxbridge. From the A40 you will see signs for Eastcote etc.
I used to live in Eastcote and I always remember fans strolling round the high street on Cup Final day wearing their teams shirts and scarves, filling in time till they got the train to Wembley.
There is a car park at Eastcote station but only 42 spaces, but there is another larger one just behind Budgens supermarket in the high street, about 200 yards from the station.
Rayners Lane station also has a fairly large car park, 263 spaces.