How about the MOD, Home Office, MAFF, Department of Transport and NHS all cough up and share a properly funded Coast Guard, undertaking SAR, MPA, Air Ambulance and Border Agency support?
We take the trained people we already have, and have one HQ. Next we provide them with an economical fleet of common type helicopters. A couple of long range FW based at the HQ, and dispersed helicopters across the UK utilising existing real estate at MOD/NHS sites.
Get them some proper boats and encourage them to work together. I don't see a problem, other than the MOD providing any procurement or management support.