You're not too late to get a funded studentship. New projects are being added to FindAPhD every day. Studentship funding is decided at different times of year, meaning that new projects are still being announced. Keep looking and keep applying. Although things do get much quieter in June, as soon as peoples degree results come out there's a whole bunch of supervisors who find the promising young student they appointed didn't get a 2(i) and they need a replacement quickly.