We had the same problem as we arrive in January and everything was so expensive! I then found a site called airbnb.com and I think its fantastic.
It is basically people who have either rooms within their houses or small apartment/granny annexes attached to their houses. Some are private or some are rooms within their houses. The one we have found had excellent reviews and we are staying in a huge double room with ensuite, sofa, tv, wir etc and its so much cheaper than any other place we found. Now obviously it might be harder if you have children but us a young couple on our own we didn't mind the house share ideas as it was soo much cheaper. When you look on the website you can filter the results to show you options that are completely private/separate apartment or room within houses. It's all professional people who own the houses not students...basically a bnb hence the website address!
Don't know if it will be suitable for you but definitely worth having a look :-)