A folkie friend of mine has a house in central Sidmouth - it is newly decorated and up for sale (should you be interested!!) but to help make ends meet she is renting rooms for B&B during Folk Week at £30 pppn. It is literally 15 seconds walk from Blackmore Gardens. There is no parking, so you'd need to leave your car at the main festival car park.
Details are on the top of this webpage:
The Tourist Information Centre TIC have their usual list of B&B houses that operate at this time of year only, but most are further out of town.