Look for/place adverts in local papers:
Free Ads
The Advertiser
The Eastern Daily Press
The Evening News
Your best bet with advertising in local flight schools is Premier Flight Training on the western side of the airport near the Air Ambulance and Police bases. The staff there are friendly and the owners manage property so may be able to help or at least advertise your case!
Try searching this site for accommodation:
http://www.norwich.gov.uk/ Hope this helps
Craig