True!
This is from
Exeter Airport "London and other UK mainland airports are not served by Exeter International Airport at present."
So BRS and a car hire. The train service would be much longer as BRS is already south of the city by some distance and you would be doubling back on yourself in a taxi or a bus to get the train and then pass the airport again. The M5 is very close to BRS and you could be down the road quite quickly.