I have just seen a project I want to apply for. However, the deadline is the 27th so will only be advertised for 7 days and the project is due to start on the 1st June 2015.

Considering this is a top london university, and an extremely competitive/popular area of research, is it possible they already have a candidate in mind? This project was also advertised last year so I'm not sure why it has come up again.

I have had a spate of rejections and don't want to apply to projects that I don't have a hope of getting! Especially as I feel my referees are getting tired of uploading so many references for me.......

Would you maybe contact the supervisor and try to suss out what the situation is?

It could be someone has dropped out/moved on.