The MAYDAY and PAN calls are used to indicate to ATC that assistance is required and UK controllers respond to such calls appropriately. If a pilot simply indicates to ATC that he requires priority for medical reasons we are required to ask if he is declaring an emergency. If he does not then we are not required to take any action. In reality, if someone tells us they have a sick PAX we don't muck about; we get him in fast.
Ambulances are called as in any emergency situation, usually by the operating company but sometimes by ATC if necessary.