I'm at the limits of my understanding here, but as far as I can determine integrity control comes from 2 sources. 1. ABAS which incorporates RAIM and the normal multi-sensor FMC operation (called AAIM) 2. The GNSS/SBAS signal itself which in the case of EGNOS is the SoL signal as far as RNP APCH is considered. Failure of either #1 or #2 will give you an integrity warning. I believe that RNP APCH requires system integrity control (#2, in other words independant from the aircraft equipment) in order for the approach to be published, it cannot just rely on #1. But I'm really at the limits of what I can find in documentation. Lack of agreement about SoL, for instance, seems to mean no NOTAMs are issued when service is expected to fall below Annex 10 standards in that location.
I have to say I have no confidence in the CAA getting it right. I mentioned the loss integrity control issue implying loss of RNP APCH to Rob Bishworth, the CAA director responsible to Flight Ops, last summer and asked him what he was planning to do about it. He had no idea what I was talking about, it hadn't been 'flagged up in briefings'.