[London] Landlord broke a signed contract and let someone else take the flat

I went through an agency [Dexters] to get a place, went through all the verifications, sent them the deposit and first month rent. I also have a signed contract and the document for the TDS. Found out today that the place has been passed onto someone else by the owner and Dexters can't do anything (weird but okay?). While I'm scrambling to find a new place, is there something I can do from a legal standpoint? I'm relatively new to UK (moved in '23) and don't know how much it would end up costing me to pursue this legally and how long it would take to wait for an outcome on average. Any insight or help would be much appreciated, thanks in advance!

Edit - while they took the deposit, and first month rent it looks like I was the only one who signed the contract. Not sure if that makes it a much weaker case for liability.