Yes, but they aren't part time. The UK schools are 5-6 year programmes (Cambridge is the only 6 year programme there). Utrecht (the Netherlands) is 6 years or more. The Australian schools are 5 years but generally you can by-pass the 1st year.
Otherwise, all the US schools have a 4-year curriculum (there used to be a few that were 3 years -- you didn't get summers off). There are individual instances where someone has to take a leave of absence for various reasons, but they are set up for 4 years.
There are some people who have dropped down to part time status because of health reasons at Penn, but its generally only for a year (1st or 2nd year) and you have to have a pretty darn good reason. I don't think they would accept you as a part time student going in.
All of the US schools are required to meet the laws of the nation- there is a federal law that governs such things, The ADA requires that people with disabilities be afforded the opportunities of regularly abled people if they meet the requirements. I was offered the opportunity to join what MSU designates as the "extended curriculum" when I started this year (I had some medical problems come up just after school started). The drawback is that there is nothing that can be done about clinical rotations- you have to do your 60 hours/week! A friend of mine who started at Davis this year is allowed to take one of her classes from each quarter over the summer so that her regular school year is less demanding ( she has a learning disability).
The short answer is that you need a good reason- but all things are possible.