There are two separate issues with training towards some FAA thingy in the UK.
One is meeting the training requirements i.e. the stuff in the logbook. This can be done in a G-reg, or any reg, by any ICAO instructor. This flight training doesn't have to be anything to do with the FAA! The FAA will accept the stuff in the logbook. Quite bizzare of course, because if you stand up and say you are training towards some FAA rating then you have to do the TSA stuff, but if you just go up in a plane for no apparent objective, but there is an instructor with you and you just happen to meet the FAA training requirements (say a 250nm x/c airways flight, for the FAA IR) then TSA doesn't come into it. You may as well call it "recurrent training"; once it is in the logbook and is signed and detailed so it is clearly authentic, it will count towards the FAA requirement(s). The last 3hrs in the 60days before the checkride can probably be done this way too; the key is that you have to be signed off by an FAA instructor as ready for the checkride; there is no requirement
AFAIK that that particular instructor had to fly with you at all (although in practice obviously he will want to).
The other is the checkride. There is a problem with examiners coming over, DfT permission requirement etc etc and people normally just go off to the USA for this. And one would do the last 3hrs (or whatever is needed) out there. There have been some recent developments (Elstree I gather) on examiners coming over but I am not up to date on this. They have always been "available" at cost plus all expenses; OK for a checkride in a Citation for example but works out very expensive for one candidate, especially if the weather is bad when he is over here...