I did Silverstone yesterday and it was pretty warm out. It certainly took me by surprise.
First, congratulations, you finished even though it hurt. that deserves some praise. 
Second, I agree with Cougie, you need to be regularly running over distance in order to build up the stamina. Keep these runs at a steady pace, slower than race pace, they should be long but you didn't ought to be hurting as much as you probably do today. Maybe cycle them 10, 12, 13, 14 repeat, varying the distance and having some harder and easier weeks.
Third - in order to run faster, you have to run faster. That means doing some shorter distance speed work. Personally, that's the bit I can't do by myself, but I go to a club for that session each week. Something about being a group, peer pressure, being urged on, what ever it is, means I will push.
I don't claim to know the specifics, but it has seemed to me that having found I can run faster over short distances, the speed over the long distances also creeps up. Maybe it's knowing you can push just that bit further and survice. But make sure you've got the mileage base to keep the stamina up.
Just to show I know what you're going through, last year I ran my first half at Silverstone, in 2:37. This year I took 20 minutes off that and I'm sure it would have been 1 or 2 more in slightly cooler conditions.
Good luck at Stratford.