Definitely look at all options. I have a one week scheme coming up, and have booked a travelodge which only cost me £400 in central london for 6 nights sunday-saturday. This isn't a summer scheme so student accom and airbnbs are less available, but even if those that are I'd still rather a hotel. Don't have to worry about clean sheets, safety, sharing a bathroom or anything like that. Of course for a longer scheme you might prefer something more permanent with your own kitchen etc
For me the firm is providing £200 towards accom, in addition to £600 pay for the week which isn't bad at all. But yeah some firms don't cover anything. I had a 3 week scheme last year, payed just over £500 per week, with no additional support for accommodation. Pretty much everyone who didn't live in London ended up many hundreds out of pocket.