Hi,
Have you seen the accommodation list on the BGS website? The cheapest and probably the best geared toward students are on there, along with distances from the school. I stand to be corrected but the cheapest I've heard of are in the £15/£16 per night band. I stayed at Maxmills Farm recently for the brush up course, just perfect for studying.
Also, check out the BGS forum on their website as there are plenty of comments from students on accommodation experiences etc.