I am currently on a placement and will be completing my clinical Biochemistry degree next year. I was wondering whether there are PhD studnetships which are run jointly at a university and industry?

Yes there are. They are usually based at a University but have industrial funding (a CASE studentship) and some of your research time can be spent within the industrial labs. It is also possible to do a PhD entirely within industry funded by the company (ie AstraZeneca). The money for these is usually quite good but they are a little harder to get on.