Faa / Jaa Ir
The FAA IR is needed to fly N-reg IFR but it is much less expensive and onerous to obtain (cheaper flying, landings, examiners fees etc.). Basically 40 hrs IFR flying inc 15 hrs instruction and some ground school. (you get credit for past IFR time including from the PPL syllabus. It also gives you an IMC on the back of it so that you can keep Mrs Echobeach happy around non airways UK airspace, at least and until EASA kills that (or both) off.
You can get a foreign pilot cert on the basis of your JAR PPL or simply do the minimal instruction and check ride for a standalone FAA PPL.
You don't need the hearing test that is required in UK at least.
You do need 40 hours of cross country time and that in FAA land means more than 50nM.
I have seen a post on here where it was suggested that an ICAO compliant IR (FAA) could be used to fly IFR on G-Reg. But I can't yet verify that that is true and if it is why it would not work in reverse (though there would not be much of a queue)
The JAR IR requires you to do a considerable amount of groundschool (as much as 850 hrs dependent upon your start point) and costs a lot more (groundschool costs, aircraft landings and examiners fees several magnitudes greater than the US etc.).
Unless you have longer term plans why bother and why shell out the additional cash ?
Good luck either way