Woofgang's link has got it covered but you might find this summary useful too:
https://nationalcareers.service.gov.uk/job-profiles/psychiatrist
Note that the entry requirements (of 5 'high grade' GCSEs and 3 A-levels, including Biology and Chemistry) stated there are an absolute minimum. Many medical schools expect candidates to have at least 8 'high grade' GCSEs and possibly 4 A-levels (all with very good grades). It's not uncommon for medical schools to insist upon candidates having Maths as one of their A-level subjects.
If you find the idea of having to qualify as a doctor first, before you can become a psychiatrist, you might like to consider a career as a psychologist instead. (The two areas clearly overlap). Then you could follow your A-levels by studying Psychology at university, allowing you to miss out on full medical training:
https://nationalcareers.service.gov.uk/job-profiles/psychologist