I brought my medical records with me when I registred with a practice here. At the first appointment, the practice nurse wouldn't touch them. She told me to take them home and make a seperate copy to bring with me, as the NHS has a habit of losing paperwork.
In terms of getting prescriptions filled here, I have a medication that I take chronically. I told the GP at my first appointment, showed him a copy of my record with my diagnosis, and he instantly wrote me out a new prescription for the British equivilant. At my next appointment, he did do some bloodwork to see if the dosage needed to be adjusted (as it is a different brand than I had been taking), but it was no problem to get that initial prescription.