I am not sure if there are particular internships that offer both clinical experiences as well as research, let alone bench or clinical research like we have in the U.S. Usually, the internship/organization/group provides one of them, and you have to seek another on your own independently.
For instance, there are some NGOs running to provide clinical exposures, but they normally don't provide any research opportunities. The NGO I went with in eastern Africa connected me with a CDC-funded male circumcision program in a slum, and due to a lack of staff there, they trained me and let me assist with surgery stuff under their one-on-one supervisions (basically holding forceps still while the main clinical officer does all the work). However, I did not do any research there but if I wanted to, it had to be done on my own. The group could have helped me out and connected me with right personnel, but it had to be driven by me independently.
Meanwhile, for my cancer research during a semester abroad, I basically went up to a doctor from overseas who attended a previous cancer conference and gave a talk a few months prior. I went up to the doctor and asked if I could go to her country and carry out a research project at her hospital. Sure, I did not get paid and had to apply for other scholarships to support the trip partly. While carrying out the research project, however, I shadowed her surgeries and community outreach programs, because I simply asked her if I could do so and she told me I could. It was all done through connections, rather than arranged by a group or organization.
In short, of course, at the end of the day you can probably do both clinical exposures and research in UK/France. However, unless you are talking about groups like WHO (even then, WHO only provides research projects, not necessarily both clinical exposures and research, at least in Geneva), you probably won't find a legitimate research project given to you by an organization as well as a legitimate clinical experience arranged by a group, at least from my experiences.
If you are talking about bench research or clinical research in UK/France, I don't know any group off top of my head. You should probably contact those institutions directly and see what you can do. I am not sure. Do you have any particular connections to those countries, or you just simply want to visit there? If there is already an existing exchange program in your institution with UK/France, that might be the first step. After that, you contact people and hopefully some will reply you back.
