a Question.
You are inbound to a city airport in a twin and you shut one down. You decide not to declare "Mayday" or "Pan".
UK ATC can declare an emergency situation even if you don't, there are other people to consider and not just those on the aircraft.
I would ask that you consider both the wisdom and the legality of intentionally flying over a congested town or city on "one"......can you land in a field?
If an emergency is declared it allows ATC to bring into force an awesome range service provision.....traffic ahead will be moved....danger areas can be closed down and overflown.....certain restrictive route requirements can be circumvented.....preferential runways made available.....a discreet frequency with your own dedicated controller to offer every assistance [or valuable silence should you need it]....continuous co-ordination with and monitoring by military agencies with massive resources to call on.....and most importantly the protection for the pilot against a raft of possible infringements such as the example above.
If you do not declare an emergency there will be no preferential treatment at all.....NONE!