The state of licence issue will be the state that holds your medical records - if you already hold an EASA class two then if you want a UK CAA issued CPL then you should transfer your medical records to the UK CAA to hold. This will You cannot hold, to the best of my knowledge, an EASA class 2 in one country and a Class 1 in another.
By now, I would have already completed my Class 1 initial. Just think about all that time, effort and money you'll have wasted should you suddenly discover a previously undetected medical issue that stops you holding a class 1 - it does happen!