No; the CAA has no right to add restrictions to EU regs. So this is a mystery; it appears to be extremely poor (or wishful) drafting.
MM_flynn's points above also remain, so the whole thing makes little sense.
In the commercial context, you are talking about AOC ops, and they would be exempted, otherwise e.g. a Brit could never get a job with Continental and fly an N-reg 747 into LHR. Quite where such an exemption appears in the ANO, I have no idea. I suspect it has never actually existed but for obvious practical reasons nobody has bothered otherwise all airlines would have to employ 100% own citizens/residents.