In this case, first, you want a live tube map with Google maps underneath.
Live train map for the London Underground (yes, those are the trains moving on the map!)
As you can now clearly, see, this gives you a couple of options - the District Line (Green) and the Central Line (Red).
Upminster (end of the District line) is your closest stop there.There is a parking lot right next to the tube station, with a couple of hundred parks. The Google Maps satellite view shows that during the day even, this isn't totally full.
Epping (end of the Central Line) is your second option. This is just near the junction of the M25 and the M11. It too, has a big parking area next to the station. The downside here is that on Google Maps, it's showing as completely full.
Of course, you can't know for sure what time of day these images were taken.
Personally I'd go for the Epping one if you're getting in early - the District line is one Londoners will not usually trust for reliability, and if you're early enough you won't have to worry about the car park filling up too much. It's also conveniently close to your M11 turn-off junction.