In general in non airworthy situations a request for priority may suffice. I believe an atco would be of assistance in order not to clog up his airspace. failure to get the necessary would entitle and upgrade to pan and so on.
In the UK there is no 'request for priority' just as there is no 'fuel priority'. It follows that there can be no 'failure to get the necessary' because a procedure already exists to 'get the necessary' this is what the states of emergency are for! As I have previously stated in this thread there were only two options and they were Pan or Mayday. In this instance the pilot required immediate assistance, by the definition I had already posted that equals a mayday.
Roghead:
The ARCC is ALWAYS informed of all emergencies in UK airspace, its part of the D&D controllers checklist. The rescue choppers are invariably scrambled 'just in case'. Little point in having rescue teams available sitting in the crewroom awaiting a call when there's potential that they'll be required instantly.