I've been to about 100 airfields in the UK, and I can only think of two that want you to call for engine start - Filton and Southampton. At both, they let me know in advance. Southampton pointed out that they might have to keep me waiting for a while, so it was better not to start up if that was the case...and in a helicopter running is expensive and starting up and shutting down takes a while, so I appreciated it.
So basically, if you're somewhere largish with full ATC, ask when you book in. Otherwise you might as well forget it.