Contract buy-out issues

Hi all, just wondering if anyone has had a similar issue to me? YouFibre mentioned to me that they offered a contract buy out, so I could be reimbursed for the termination fee from my previous provider (Sky). So I made the switch.

Fast forward to today and I have received my latest bill from Sky with my fee on it. I e-mail this to YouFibre as proof but they refused it claiming it is not a "Final Bill". Problem is, I will never receive a "Final" bill from Sky because I still have a TV package with them. The response I got from YouFibre was as follows:

Thank you for sending over your November and December bills. I can see the credit for the cancellation/termination noted in November, but unfortunately, for the contract buy-out process we specifically require a final bill document that relates to the broadband service only.

Because you still have a TV package with Sky, they may be able to split the bill and issue a final bill for the broadband portion. This is rare, and I understand it may not always be possible, but without that document we are unable to proceed further with the buy-out.

I’d recommend contacting Sky directly to request a final bill for the broadband service. If they can provide this, we’ll be able to assist you right away. Without it, I’m afraid we won’t be able to move forward.

I've contacted Sky and their response was that this is their standard format for their bills and that it had never been an issue in the past. It seems they are unable to change the bill to meet this request.

I feel like I'm a bit stuck and SoL. Am I right to be upset or am I maybe overreacting a little? £250 is a lot of money to me and I thought I would get this back, otherwise I would have never have made the switch. The terms + conditions mentioned a "Final Bill" on their page but perhaps that my fault for not really understanding. I just assumed it would mean the bill with the final payment for broadband.