Hey
Depends on specific applications, positions and postgraduate courses.
I had to put my A-level grades in each of my doctoral applications (PhD and Professional Doctorate in Health Psychology). The current application for the clinical psychology doctorate includes a question on A-levels (and I think there's space for an A-level equivalent). But further up the academic ladder, university marks/classifications become more important.
Clinical Psychology is only one option for psychology graduates. But, yes, clinical psychology is very competitive and some universities look at A-level grades to select candidates. However, people with poor A-levels or no A-levels (ie access to university courses) have got onto clinical psychology doctorates with excellent university marks and relevant experience.
For clinical psychology doctorates, some universities (such as UCL and Bath) look at A-level grades and factor in good A-level grades whilst selecting the top performing applicants for interview. Other universities place more emphasis on experience and good marks at universities. Also, consider that some universities implement selection tests before interview and they interview the top % scores in these selection tests. So applicants performing well in the selection tests could be invited to interview, despite any lower marks. Although, in the cases of applicants with tied and similar scores, I think they select applicants with the strongest academic marks and experience.
Other psychology doctorates are less competitive though.
Friends of mine have got onto the clinical psychology doctorate with good A-levels, good university marks (2.1 at undergraduate level), master qualifications and excellent relevant experience. One friend got on with a First at undergradaute level, an MSc a PhD and relevant experience. If you've got good university marks, relevant experience, strong references and interview well, then you maybe in with a chance, but it also depends on competition from other applicants.
Best of luck