Hey, mate. A little more info needed here...
Firstly, what mode of transport do you need? I'm gonna go along with trains, assuming that you're from outside of the UK and haven't (to my knowledge) rented a car.
The last train from Exeter to London (Paddington) is at 00.59 and takes nearly four hours, getting you in at 04.49. If you can find a place to crash in Exeter, there's a train at 05.46, taking a bit under three hours. And there are later trains that might be suitable dependant at what time you are leaving the UK...
A little more info, eh? What time to you need to be at the airport? Is a hotel stay in your budget?
EDIT - forgot to answer your original question! 8pm start, which usually means NMA will be on at about 9pm or thereabouts, so an 11pm finish would be about right.
