B&Bs - there are two or three down near the Wheatsheaf/Premier Lodge and Sun Inn (on the old road to Basingstoke, about 2 miles away). I'll try and dig out a number - they all recommend each other when full so if I can find one number, that's all you need. It's about £25 for B&B and sometimes includes a lift up to the airfield.
(I know the event is on the Popham calendar as a radio operator looked at it and asked me if I knew what type of aircraft a "Pee-Pee Rune" was).