Meh, everything but the hotel room sounds fine, assuming they are paying for your travel back every weekend? Hotel sharing though, with anyone, no, with some hot intern.... no, you'll end up fired, with some huge obese nasty smelling person you actually dislike, absolutely without question NO.
Firstly, is this a job you desperately need or will care about long term. IE if you're finishing your masters this summer and will be looking for a new job, does it matter if they stick you with bad jobs for another couple months, if you expect to work there for another 2 years thats different.
How much is a hotel room, how much do you get paid. If you took the £20 extra a night and paid another £20 for some travellodge room, would you be losing money or only losing a little to keep a job you still want.
Don't suppose you know anyone in London you could stay with for a few months instead?
As for Laptop, beg/borrow/steal one.... hmm, could look into local uni's to see if you can rent a student room over summer/use computer labs for work, etc, etc?