Some universities do, yes, but not all. You're asking in the Medicine forum though - you'd probably get more accurate answers if you asked some biomed students (though there will be some grad medics around here who did Biomedical Sciences for their first degree).
Do you have to do dissection in the course? And what A levels are needed for it?
I had a friend who is studying Biomedical Science at Bedfordshire.
If I recall correctly, there were some dissection but she took the choice to just watch.
She's had stuff to do with Biology and Chemistry, so I suppose those would be good subjects to study, though I would recommend looking at the entry requirements for the universities you want to go to, and then maybe ask about those particular courses and what they do with regards to dissections.