What callsigns do UK Medical Emergency Response Teams use?
Civil

For the UK as requested, this information is in § 2.32 of the Radiotelephony Manual (CAP 413). The call-sign for a Helicopter Emergency Medical Service (HEMS) is three parts:


HELIMED
Two-digit identifier unique to the aircraft (list on Wikipedia).
Suffix A or E


A for a helicopter en-route to an emergency or to a hospital with patient(s) on board
E for positioning back to base (a lesser priority than A but higher than the other traffic).



If the helicopter is responding to a scene, it can be pronounced Helimed 7-7 Alpha, for example. Note that Wikipedia lists three-digit identifiers for some helicopters, contrary to what the manual says.

Military

From § 2.44 of the same manual, the call-signs are 'rescue' and 'rescue helicopter', suffixed by the mission number. This is for search and rescue (SAR), no distinction is made for a purely medical mission in the manual.