Faa Ir
I did not have the luxury of a UK based plane but spent a couple of weeks getting my IR in California and would recomend the process over trying to do it here in part or whole despite the fact that the past "time" counts.
As for cost it can vary - I paid $130 for my TSA approval and another $40 for fingerprints that can rise to over $100 if you are unlucky and add a week to the process if you don't go to a location with online submission (TSA offices are good).
No charges for approaches and no need to call up three weeks in advance for a slot- I reckon that the flight there and the cash to get through the TSA are more than offset by the savings in that alone.
A big benefit was an FAA approved advanced training device that was loggable and made the process of repeating some manouvres much more efficient bot on the wallet and in learning.
I would disagree with IO540 on the 2 weeks if you know your stuff beforehand and 3 weeks on a glass panel. I think in my case it is more likely the other way around. I had basic knowledge before I went and learned on a glass panel which I felt assisted by reducing the workload while it was sinking in so that I accomplished the 35 hours additional time required in two weeks. I am conscious that I now need some time making it all happen in steam world and guess that might be the extra week that IO540 refers to.
Have fun.
check your PMs too.