Julian, I am not sure you would knock off the FAA IR in just 2 weeks if you have zero instrument experience.
I did it in 2 weeks (26hrs total dual time) but I had ~ 500hrs, incl ~ 80hrs IMC time, and the IMC Rating from about 4 years previously. It was damned hard work and I was totally knackered every day. Yet, before starting, I considered myself to be a competent instrument pilot, able to fly any approach straight off the plate, and fully capable of European airway flight and procedures.
My estimate for a totally ab initio FAA IR would be 4-6 weeks.
What seems to be a very common path for owner-pilots I know personally is
UK PPL
UK IMCR
FAA PPL/IR (you get full credit for all your previous training on this)
Buy an N-reg plane
If N-reg is not available / not desired then
UK PPL
UK IMCR
FAA PPL/IR (you get full credit for all your previous training on this)
JAA IR (you get ~ 35hrs flying time credit for your FAA IR but still have to sit all 7 writtens)
offers a pretty cost effective route which I know some people are doing around now.