Cross-country is different in the USA and the UK. I can't remember the exact definition, but it's something like:
UK - left the circuit. I suppose the "Bomber command" or "International" circuits at some of our airfields might even qualify.
US - 25nm from home base. Real navigation required!
You can indeed convert a US IR to an IMC rating. The US IR is a LOT more difficult and exacting than the IMC (I have both).
You'd need several weeks to do a US IR from scratch (well, I would). It's worth doing - but to be safe, I would want to do a fair bit of "conversion" to UK/European ways if I'd not done any IFR flying here. Taking a US IR and flying IFR in Europe without further training might be "an experience".
So, my choice would be to do the IMC rating in the UK, in real UK weather etc, then use it for real (keep it current!). After you've got 40 to 50 hours *real* IMC flying in the logbook, then go and do the US IR.
Then, of course, you need an N-reg aircraft to use the IR "in anger" over here.