Which subject? Do International students not get funding for PhDs/pay fees? In the UK you get funded for 3 or 4 years, I've met one self-funded student, and quite a few International students.
I don't know what an HSMP is.
In Biochemistry an Mphil or Msc would help get you onto a PhD, particularly if it was in the lab/area you wanted to be in. As far as I'm aware research is very competitive, but if you did just an Msc in a vocational subject (e.g. genetic counselling) it is probably neccessary. It depends on the job, some require extra qualifications, some see them as useful, for some it would be no advantage.