Depends what you mean by "an accountant". With the exception of some of buildersmate's last post and also twix all the answers have immediately gone into the route to being a qualified accountant. And if that's what you meant that's fine. It IS a long hard slog though. It's pretty unlikely that without either a contact already in an accounts firm, or a relevant degree that an accountancy firm will hire you. It's a competitive market out there and there are lots of accountancy graduates already looking!
You can look at CIPFA, CIMA, ACCA or training with a licensed industry training firm but you'll likely hit the same obstacle.
However, the term "accountant" is not prtected (unlike say "Solicitor". You cannot call yourself solicitor unless you are qualified as one, you can call yourself an accountant tomorrow if you like so long as you don't claim to be a Chartered Accountant or a Qualified Accountant). I know people who made a perfectly reasonable living as an "accountant" preparing accounts and tax returns without having an accountancy qualification to their name. Plenty of ex Inland Revenue employees do that kind of thing. If you understand preparation of accounts and know your way round a tax return then you can do that. Of course, attracting enough clients to make it worthwhile is the difficulty.
If you want to go down that route then the likely best starting point presuming you don't already know about accounts is something like an HND / HNC in accounting or the Accoutning Technician option already mentioned by twix.