Cheapest quote I got was $3300 for the IR, which included 41 hrs instrument training in a 172 and Sim. This was based on 2 doing the course at the same time through a private instructor in Long Beach. You can get the IR at one of the schools out there for around $4000 including all exams, flight tests etc. On top of this you need a return flight to LA at £250 plus hotel accomodation at $38 per night. The length of time to do this course depends on the student, it is possible to complete in a week if you have done the studying prior to arriving in California, and if you're willing to do 10 hr days...but I would allow at least 2 weeks myself. Grand total: £2400 ($4000) + £250 + £320 (hotel) = £2970ish.
It is true you can do the IMC rating in the states a lot cheaper, though with the IR you can then fly IFR in the US and in an N reg plane world wide, as well as IMC on a JAR licence. To maintain the FAA IR you only need to complete a bi-annual flight test, which is a good excuse for a holiday to the US (or one of the FAA examiners in the UK). If you don't have a NR, you can do some of the flying at night and get signed off at one of the JAA registered schools if you want the JAA NR. Long Beach has a number of good schools, all with links to a JAA examiner. I would recommend Rainbow Air in LGB (www.rainbowair.com), I have flown with them before, they have good A/C, good bunch of people and don't rip you off.