I would say that clinical neuropsychology is probably the closest 'middle ground' option outside of going down the psychiatry option, as it tends to be quite a technical/biological applied psychology. At present, there isn't a direct training path in clinical neuropsychology, you have to compete the doctorate in clinical psychology first, then compete further accredited training post qualification. I think that the British Psychological society have been considering a direct entry route to clinical neuropsychology as it is quite a niche specialism.
It is possible to work in the UK as a neuropsychologist, both in the NHS and in private practice. Neuropsychologists may specialise in areas such as acquired brain injury, epilepsy, Parkinson's disease, multiple sclerosis, motor neurone disease, stroke, neuro myelitis optica.....and many other biological brain conditions. They may also work with people who have medically unexplained neurological symptoms (e.g. Non epileptic seisiures). Their work may involve assessing the impact of an individual's neurological condition on their memory, processing speed, verbal reasoning, numerical reasoning....or work may involve looking at how to help an individual who is living with a neurological condition improve their quality of life.
So a pretty diverse bag for an applied psychological sub speciality!