National Express have 5 coaches per hour into Central London (Victoria Coach Station) around that time of night. (The journey is scheduled to take 90 minutes).
However, that might not help you very much because the first coach which meets a connection for Exeter doesn't leave Stansted until 0530. Taking an earlier coach will simply leave you stranded at Victoria Coach Station for several hours. It's a fairly depressing place at the best of times; it will probably be utterly soul-destroying in the early hours of the morning!
So, if you're taking the coach to Exeter, it might be best to stay at Stansted Airport until 0530. The connecting service arrives in Exeter at 1235.
Those times are for a random date I selected in May. To check the times for your date of travel, see here:
http://www.nationalexpress.com/
If you were desperate to arrive in Exeter as early as possible, you could arrive there at 0905 (based on current weekday timetables) by taking a National Express coach to Victoria Coach Station and then a taxi to Paddington station, to catch the 0527 train. (Change at Bristol Temple Meads. Arrives Exeter at 0905). However, you don't get there very much later if you wait for the first train out of Stansted (at 0530 or 0600, depending upon the day of the week) and then take the Tube to either Waterloo or Paddington. (Services to Exeter run from both stations). All UK rail times are available here:
http://www.nationalrail.co.uk/
I've checked the Exeter airport website and it doesn't show any direct flights from Stansted. That means that you'll be forced to choose one of the above options. Personally, I'd stay at Stansted until the trains start running.
Chris