Short answer–no
Long answer–still no because…
First of all, if he has already earned a BMChB in the UK, he won’t be eligible for MD/PhD programs in the US because he already holds a MD (equivalent) degree. He could apply for PhD programs though.
However the biggest issue with medical degrees from medical schools outside the US and Canada is the need to complete a US medical residency to be eligible for a US medical license needed to practice medicine in the US.
Foreign medical grads have to go through the ECFMG, obtain a certification of eligibility, take and pass the USMLEs and then apply for the NRMP (National Residency Match Program). Non-US grads are significantly less likely to match into any residency, and those that do are likely to match only into non-competitive primary care fields (family medicine, general internal medicine, psychiatry) at non-academic programs.
You/your son should read about the certification process for foreign medical graduates who want to practice in the US
[Educational Commission for Foreign Medical Graduates](http://www.ecfmg.org)
You/your son should also read about how few non-US medical grads actually match into a US residency. See Chart 15 on p.22 for number of matches sorted by country of medical education.
[Charting Outcomes in the Match: International Medical Graduates](http://www.nrmp.org/wp-content/uploads/2014/01/NRMP-and-ECFMG-Publish-Charting-Outcomes-in-the-Match-for-International-Medical-Graduates-Revised.PDF-File.pdf)
And you both need to realize that it’s only to get more difficult to gain a US residency since the number of US medical grads is increasing and the number of US residency positions is not. It estimated that by 2020, all US residency slots will be filled by US medical grads.
[Residency Training and International Medical Graduates: Coming to America No More](http://jama.jamanetwork.com/article.aspx?articleid=1475200)
Lastly, should he decide to only complete his undergraduate degree in the UK, he will still face serious issues if he wants to attend a US medical school.
First, US medical schools almost universally require applicants to have earned a minimum of 90 credits at a US or Canadian college/university, including all science, English, math and social science pre-reqs. (There are, I think 2 or 3 US allopathic med schools that will "consider" a UK undergrad degree, but even those state for serious consideration, applicants need to have taken additional US coursework. There are 8-9 osteopathic medical schools which will consider undergrad degrees from foreign colleges.)
Second, AMCAS, which is centralized application service used by all US medical schools, will not verify transcripts from non-US colleges/universities. Without verified transcripts, an application will not be considered complete and will not be forwarded to medical school. TMDSAS, which is centralized application for all Texas medical & dental schools, also will not verify/accept transcripts from colleges outside the US. AACOMAS, the centralized application service for osteopathic medical schools, will not accept or verify foreign transcripts.
~~~~
tl;dr-- bad, bad idea to attend med school in the UK if he wants to practice medicine in the US;
bad, bad idea to attend undergrad in the UK if he wants to attend a US med school