I would climb down slightly from my earlier position, and concur with bookworm.
Unless one can get a letter from the FAA allowing in an N-reg whatever the CAA allows in a G-reg (which is far from impossible, looking at some written FAA replies I've seen) it may be safer for an N-reg FAA PPL/IR pilot wishing to fly an unofficial IAP to also have a UK PPL with an IMC Rating.
However - what constitutes an "IAP"? One could argue that any descent below what in the UK is called "MSA" i.e. < 1000ft AGL except in mountainous terrain where it is 2000ft. (In fact I don't even know for sure if the 2000ft is just FAA, or ICAO, or CAA).
And one could argue that a 1000ft MDH is reasonable for a DIY IAP, anyway. Which makes all this moot. (Trevor Thom says, in Book 5, it is OK to do a DIY descent TO the MSA so it must be OK
)
It's doubly moot since the sort of place where one would be doing a DIY IAP in the UK is unlikely to have an accurate means of determining the cloudbase anyway.