Any ISP can take you over. It's just that your phone number doesn't show up in the BT Wholesale checker.
There is a slight possibility that you may not be able to keep your current phone number, (if it was a new number when you went onto the TalkTalk system), but I think even that problem has now been resolved. It is normal to be able to move both the line, with it's existing number, and the broadband, from TTB LLU.
I thought Xilo also did TTB connections - but I seem to recall at one point they had a problem with migrating people on it from other resellers. Maybe that hasn't been solved. If that's who you would prefer to go to I suggest you ask them again and get the reason if they say they can't.