What if my estate agent promised me a move in date and then changes it 2 days before we move?

My partner and I found a flat we liked and put down a deposit for it. The current tenants were scheduled to move out on May 8, but since our current lease ends on May 1, we asked if they would be able to move out early. The estate agent went back to them and they said no problem, so we signed a lease for May 1st, paid 6 weeks deposit+fees and contracted a mover for May 1st. Now today, the estate agent calls and says the current tenants can't move out by May 1 and since they are contracted officially to the 8th, there is nothing they can do about it. He basically said, sorry, but I suggest you find another place to stay for the week. Unbelievable! 2 days before we move in? What recourse do we have here? Are we pretty much screwed?