I had the opportunity to ask Swanwick today about squawking 7700 in an emergency descent, for those that don't know they are the air traffic centre that handles aircraft in English and Welsh airspace.
Their reply is that it is preferable to squawk 7700 but only after crew have stabilised the aircraft. (This fits in with the "people" part of prioritising plane, path, people.) With regards to the callsign/squawk all the original information is still retained after squawking 7700. I did not know this. A big change since the West Drayton days.