I'm training to be a Health Psychologist at the moment, so if you have any questions- ask away!
Definitely easier to obtain places on the health psychology doctorates as opposed to clinical, probably as clinical is funded by the NHS, whereas other professional routes are self funded.
From what I can remember, during my A-levels, there was continued pressure to get into the top unis, but when you graduate, there's definitely more emphasis on overall undergraduate classification rather than actual university location. For example, in some cases, someone with a 2.1 (regardless of uni )will pass through initial filtering process for some unis and jobs over someone with a 2.2 (regardless of uni!). The undergraduate classification issue was definitely not mentioned during my A-level studies, which is a shame.
Obtain relevant experience during your undergraduate studies (ie care assistant, support worker) or apply to sandwich courses with an extra year of placement experience and obtain the best overall classification as possible (ie a high 2.1, ideally a first) to stand a chance with obtaining places on professional doctorates in psychology- be it clinical or health psychology.
After graduation, look out for graduate psychologist positions (ie research assistant, assistant psychologist etc), but be aware that these graduate psychologist positions are highly competitive. Look out for opportunities to publish work in academic journals and obtain references from chartered psychologists, preferably chartered clinical psychologists for clinical psychology doctorates and chartered health psychologists for health psychology doctorates.
Also if considering clinical, carefully select unis as some unis prefer applicants with certain backgrounds and some will only look at candidates with 2.1 and above and immediately exclude anyone with a 2.2 regardles of postgraduate qualifications. Some universities have pre-selection interview tests which involve some sort of test in research methods rather than selection on application forms. . The top performing applicants are selected for interview. So perform well on these tests to increase chances of an interview.
A-level results are taken into account in selecting applicants for interview with the clinical doctorate at SOME universities (ie UCL), so probably a good idea to perform well. Admission tutors seem to look out for consistency in high academic performance in order to withstand the pressures of doctoral study.
Perhaps carefully select your undergraduate degree. Some unis contain final year modules in clinical and health psychology which may place you at an advantage when it comes to applying for psychology graduate jobs. Just ensure your undergraduate degree is accredited by the British Psychological Society (BPS).
You can always take on master qualifications to increase your knowledge base after graduation which will give you more options. Although, you will need to complete a BPS accredited MSc in Health Psychology with at least a Merit in order to proceed with a health psychology career.
Best of luck.