If you do the 5 or 6 year medical education in the UK, you will need to pass the USMLE to practice in the US. Although this is relatively similar to finals, it is an expensive process and not everybody passes (by any means). Furthermore, as an international student, your education in the UK would be pretty pricey and the work situation is unclear at the moment as the British Govt is trying to limit the job opportunities of immigrant doctors.
If you do a BSc here followed by an MD or DO in the US, your British degree may not carry enough of the material required for pre-med. I'll admit my knowledge on this is practically non-existant, you may need to get advice from a US source on this.