Cat3C,
When I started at LGU, I had digs in London already setup. However, there was a large number of danes starting at the same time and none of them had accomodation sorted. Basically, it took most of them about 3 weeks to sort themselves out, and in the mean time they were living out of suitcases in hostels. I can only suggest that you spend a week or two before you start seeking out accomodation as this will save you no end of trouble. Although the LGU has an accomodation list, your best bet is to get yourself a copy of Loot. It has a huge list of rooms going for rent in london and should give you an idea of where and what you can get for your budget.
For LGU, look at the east end as it's cheap and fairly easy to commute into tower.
All the best.