Some employers will accept trainees who've got good a good general education (perhaps five A-C GCSEs, including Maths and English) plus general office skills and experience. (So that means ensuring that you're proficient in the various aspects of Microsoft Office. Additionally, some employers might seek staff with experience of Sage, especially if they're going to be dealing with payrolls).
Within some organisations it might be possible to progress to the top without formal qualifications but most employers would probably expect their senior HR staff to possess a relevant degree or CIPD qualification. Larger employers may encourage (or even require) their staff to study part-time at college, funded by the employer.
See here for further information:
http://careersadvice.direct.gov.uk/helpwithyou rcareer/jobprofiles/profiles/profile748/
Chris