I'm from the UK and applied to med school after doing one degree already (most of us don't do this here, but a sizaeble number do) and yes, they wanted to see my high school exam certificates (comparable to your transcript.)
UK medical degrees fall into 2 categories:
1) Those for people with degree ("graduate-entry programmes" or "GEPs") - 4 yrs
2) Those for people straight from high school OR people with degrees. - 5/6 yrs.
(ie if you have a degree you can apply to either or both types.)
For a course of type 1, depending on the uni, you may have to have a life sciences degree (which includes a number of majors eg biology, chem, psychology sometimes, biochemistry, anatomy.... it depends on the uni as to which they accept) or you may just have to have any honours degree. Again, some GEPs require a life sciences degree (eg Cambridge, Barts) and some don't (eg Oxford, Kings.)
These courses will want to see your high school AND university grades.
For type 2 courses, the fact that you have a degree MAY mean that some of the high school requirements are waived for you. This is certainly the case for UK applicants - they lower the grade requirements, but it would be rare that they would actually say you don't need the 3 science subjects, they'd just not insist on you having top grades for them.
Basically though, for both types of course, you will need to send any uni you are offered a place at a copy of your transcript. They don't want to see this for you to make the application however if a school (after interview etc) makes you an offer, then to confirm the places you would have to show evidence of all the grades you stated that you had on your application form.
You should contact each school you're interested in applying to and ask them what they require of US graduate applicants to their course. The admissions offices are usually very quick to respond to emails and really know their stuff.
If you have any more questions about UK uni's then I'd be happy to help
Jane (<-- British!)