Depends on med centre/unit, it is possible for your computerised record to move from one system to the next. The DMS has been able to do this for years, the NHS have only just started to do this (pilot project already started with a 500 extra GP Practices starting to do so this year).
This project will probably extend to the DMS, when the new med system comes online, with your NHS record miving onto the military system and vice versa (maybe after a little cleansing).
1. Just a phone to see if Med Centre X has your records
2. a few key presses by them to export the record
3. maybe zip up the file and email it on (or use a shared drive on the receiving system)
4. receiving system saves off the file
5. finally a few key presses to import the record