The answer depends on what you want to achieve.
The FAA accepts ALL previous training, anywhere in ICAO, towards the logbook requirements for the PPL, IR, CPL, ME, ATPL, whatever. Some UK based FAA training outfits will say otherwise because they like to make money
So, the expression "conduct instruction for the FAA Instrument Rating in the UK" is not really applicable.
So, one can train towards any FAA license or rating with a JAA FI, in a G-reg! Yes, it's true. It would pay to write next to each logbook entry what exactly it was, in FAA terms, e.g. if doing a 250nm x/c flight it's best to make that clear. That flight needs to be airways and needs to have 3 landings with different approaches, and much fun has been had debating whether all 3 need to be done on the same day, and a logbook entry specifying exactly what was done (NDB, LOC, VOR) will be very helpful.
But the student's logbook must be endorsed as ready for the checkride, and this must be done by an FAA CFI/CFII. He also needs to have has 3 hrs of instruction in the 60 days preceeding the checkride, and traditionally this is done by the FAA instructor signing the logbook, so for the last few hours you do need to be an FAA CFI.
There are bigger issues with FAA IR training in the UK however.
Start at the back end: the FAA examiner (whether a DPE or an FAA salaried one; the latter is now very rare outside the US) will require an N-reg for the checkride. This means needing the DfT permission, which in turn requires the candidate to be an owner or part-owner (see the DfT website). So, one can't run a "school" on N-reg planes, unless the DfT gives permission which is possible but not likely. You can really train owner-pilots only. The alternative is to do the checkride outside UK airspace.
You need to get DfT permission for any paid training in a foreign reg plane in UK airspace. This is readily granted, and is free. The alternative is to not charge for the training, or do the training flights outside UK airspace.
For the PPL or the IR (not for the CPL) the FAA CFI/CFII needs to be registered with TSA even if UK resident. But if the training is done in a G-reg by a JAA FI, and the flights just happen to meet FAA requirements, TSA doesn't come into it
There are plenty of FAA CFIs around the UK. The hard bit is finding an examiner. Over the years, loads of people have been up blind alleys, shelling out £££ for training and then not being able to get the checkride, and having to go to the USA to finish off. And don't I know it