Quite simply the firm behind Coppergate have broken their contract and have to give you your money back there is no 14 day you have to give them in these circumstances.
The firm behind this must have known for months this wasn't going to get completed on time. It was obvious to those of us living in Swansea that was likely to be the case. I spoke to a construction worker on the site back the beginning on July and he told me then there was no prospect of this being completed on time. Personally I think it will take 2 months to be fully completed. The company involved should have been advising you and others of the actual situation. Instead they chose to say nothing until last week in an effort to keep their clients.
There are other options you could take if you so wish.
Student roost still have some rooms and I gather Swansea University have rooms on the student village and I believe offer free buses. Oldway might still have rooms available and you could also look at GLC properties and Student Digz and Swansea4Students. Have a look at the other thread I prepared on the Swansea University forum.
Some of the options may be more downmarket but they will at least be available now. This company simply doesnt deserve clients. They have let prospective students down badly and I feel very sorry or others. Student Roost and Oldway I believe will be offering Gyms on site. There is also a really nice cheap gym in town called the Gym which is far bigger and better than the YMCA you are being offered.