I would probably just for the less hassle go to Gatwick and get yourself a class one medical. Least you then won't need the hassle of transferring it over. I had this issue a year ago and took 6 weeks and many phone calls to get it sorted! Also as far as I know ( may be wrong ) but with the new EASA medicals you can get it issued from another state. Although this is just pure speculation on my part. But I fly on a non UK licence using my new EASA class one issued in the UK without any trouble