I agree with Kim above, consider doing the AAT course. It is well regarded among accounting firms and is also a good stepping stone if you wish to pursue any further professional qualifications.
Also, look for part-time work with a firm of accountants to gain practical experience. Try to find one that offers the opportunity to learn a range of different things; bookkeeping, accounts, vat, payroll, tax returns.
Focus on being accurate first, then speed. You will get quicker with experience and confidence. If the person you are doing work for can see you are accurate then you are more likely to get a wider range of things to do, which is what you are after. It's ok to make mistakes, we have all done it, as long as you learn from them and don't repeat the same ones.
If after gaining a few years experience and knowledge you decide becoming an independent bookkeeper is not for you, then you will have learnt useful, valuable skills you can use if you decide to start a business doing something else. You will have an advantage over many start-ups as the lack of financial skills are often a weakness in many small businesses.
You will also be valuable working with or for someone else too.
Good luck with whatever you decide to do. I'm sure you will do very well.
