Summer accommodation in London - where to look?

I've got a few internships and family events coming up this summer and I'm looking for summer accommodation from around early July to mid-September. I want to rent a room all the way through, as I go to uni in the North and don't constantly want to have to shift all my stuff around. My budget is fairly high, but I'd rather not spend more if possible. Location isn't too much of an issue as I don't mind taking the Tube, so long as the area's safe. I would rather be fairly central, though.

Any recommendations on where to look? Have tried KCL/LSE summer rooms etc. but can't find anything available on the dates I want or even close to them. I was thinking of trying private accommodation as well.

Any suggestions would be really helpful, thanks :smile: