Hello and greetings from sunny Leeds!
I am not in the medical profession, but I have a number of doctor/nurse friends working both for the NHS and private practices. They suggested to have a look at the NHS website, where there is a special section on applying for positions from overseas - it's
http://www.jobs.nhs.uk/overseas_cand.html- the website is good for general info on the NHS. They all said there is a huge shortage of medical professionals in the UK, so you should be in demand!
From my experiences of private healthcare in the US and public healthcare in the UK, there is a huge difference in terms of patient expectations and hence working practices, but from my observations, nurses seem to have to work really hard for relatively small amounts of money in both countries in both systems (but I guess you know that!).
Here in Leeds, there are several large NHS hospitals, run by the Leeds Teaching Hospitals NHS Trust and a number of private hospitals (Nuffield and BUPA are the main ones). There are also nursing employment agencies, who should be able to help you find work - see
http://www.bupa.co.uk/healthprof/ and
http://www.firstpointhealthcare.com/ - although I think they often cannot be bothered with having to go through all the visa stuff - give them a go anyway.
Good luck and hopefully you'll soon be in Leeds!