Can't speak for Brands, but there are a number of cheap (ish) hotels within 15 to 20 minutes of Silverstone. Look at Milton Keynes and Northampton - there are chain hotels in Towcester and just down the A43 towards Brackley (the Green Man) but they mysteriously raise their room rates when events are on...
There's also a number of decent B&Bs close to the circuit too.
I can't recommend a specific one though as I usually go home
