All UK SAR aircraft use the callsign Rescue **, with the stars being numbers.
As you can guess from my handle, I'm involved with SAR as a voluntary Coastguard (aka dope on a rope!). Most of the helio SAR in sw England is done by RN Sea Kings from 771 Squadron (grey a/c with red nose and tail with Ace of Clubs insignia). These use the callsign Navy 193/194 etc. when on routine duties, but as soon as they've been tasked by RAF Kinloss to SAR duties, the callsign changes to Rescue 193/4 etc.. If they're tasked to a job, more than 150 miles offshore, 2 helios are always used, usually with a Nimrod providing extra cover and overseeing the op.. RAF Sea Kings out of St Mawgan (I assume they will no longer be flying out of St Mawgan now the RAF have pulled out) and Chivenor use 169 (and 170?) callsign. The RAF SKs are fitted with FLIR equipment, but the Navy's aren't, just the No. 1 eyeball. The Devon & Cornwall helio calls Oscar 99, and I know some other Police units also use 99 calls.
When an emergency situation arises, Falmouth/Brixham MRCC (Maritime Rescue Co-ordination Centres) have to contact Kinloss and request Navy/RAF assistance. Officially, they cannot task Navy/RAF units directly, but a phone call is made to the bases to give them the heads up, which saves 10 minutes getting kitted up and the aircraft wound up. The Navy and RAF usually get alerted before our pagers are pinged! and more often than not, they can get to the scene before we can (especially in the summer, with tourist drivers who are driving down the middle of the road at 20mph, rubber-necking the scenery, paying no attention - they're on holiday and leave their brains at home - rant over!). We also work with the RNLI sea-going and inshore lifeboats, Police, Air and land Ambiulances/Paramedics etc..
Also at RNAS Culdrose (HMS Sea Hawk) there are Sea Kings used for submarine detection, Merlins, Jetstreams and around 10 Hawks, flown by ex-RAF personnel to simulate enemy aircaft and missile attacks on Navy vessels during exercises. Very rarely is the Hawk's front seat occupied, so I'm still working on trying to bum a ride!