I think it depends on location really. As up until Bristow came back into SAR the Coastguard had the full responsibility of scrambling and the ARCC used to go through the Coastguard for tastings.
It's the Coastguard that still pages the crews when on 45mins standby.
This is still the case on the South Coast.
The ARCC will eventually, sooner rather than later head to the National Maritme Operations Centre, near Southampton and be under Coastguard Control.