The primary role of SAR is to save lives, civilian or military is irrelevant.
There are currently 12 assets (11 overnight) to provide coverage for 65M people. That's 1 helo for every 5M ish, which is pretty thin coverage at times, especially if ageing aircraft produce poor serviceability or bad weather precludes flying.
Each task is judged on it's individual merits by a human being before any asset is committed. That said there are currently specific rules on how to react to a "Mayday" from an aircraft, which are almost automatic and pretty much puts you at the top of the pile.
Whether this approach will be adopted by the Coastguard when they take over I couldn't say, I'm not that close to this particular coal face.