The UK has a very active research community in medical physics, biomedical engineering and related physical sciences. Some research activity has close links to healthcare provision, and is embedded within the NHS environment, and some is a step removed and looking ahead to future developments.
The starting point for a career in academia is a postgraduate research degree (PhD or DPhil), and the https://www.findaphd.com/ website under Physical Sciences is one place to start looking. Or look at the Engineering and Physical Sciences Research Council (EPSRC) website. EPSRC is the main UK government agency for funding research and training in engineering and the physical sciences, investing more than £800 million a year (in a broad range of areas from mathematics to materials science, and from information technology to structural engineering).
You will need to do some research to decide which area would interest you and apply for funding of course.
The options after a PhD are to stay in an academic research based role as a Post Doctoral researcher, or to apply for lectureships. If your PhD has some relevance to Medical Physics and Engineering you can still consider applying for the STP Training (which is not unusual) or consider the Route 2 / Equivalence option if you want to move into a clinical role. See the FAQ question section on the right for more information on Route 2.
Please note that if you are considering a purely academic non-clinical career, you do not need HCPC registration.