I think probably, though you may not. In my experience though it is easier to do everything through the one system so I recommend you do. Ask the aeromedical centre to send your details to the CAA, look on the CAA website and you will find a form to convert your medical. Ensure the IAA know you are only changing your medical and not your state of licence issue as unless you can prove you now live in the UK, you will not be entitled to do this.