Technically, yes. All you need to become an actuary is maths A level (at B grade or above, I believe). I did a lot of research into it and found that, whilst many firms ask for a quantitative degree, there are still plenty that don't. My advice is to go on the Actuary Profession website and look at the list of employers - there is a directory with employer profiles and it's quite useful (it's also arranged first alphabetically and then by location). Research to find which ones might take you.
Try to get some work experience whilst at university (if possible - I don't know if it is) and perhaps do some extra maths-related study. I read somewhere that it's a good idea to try to take one of the actuary exams before you start applying to places so that they know you're a) serious and b) good enough, as the exams are hard to pass. However, the actuary textbooks seemed pretty expensive when I looked into this. Ebay might have some though!
I did go to a PwC event once and asked a man there about my chances with the profession (I did English), and he was blunt and said I'd find it a struggle (although I think he was specifically talking about PwC). He suggested applying to enter the firm through another route (audit, assurance, etc) and then moving departments if I decided I still wanted it.
Also, I spoke to a chemistry grad who had become and actuary and she was quite positive about my notion of becoming an actuary. I hope this helps a little bit!