In order to try and protect children and give you the best chance at a good education, there are certain rules that have to be complied with. The government is basically acknowledging that you do want the right to earn money, but also that you need to be restricted so that you are not trying to do too much, letting your education suffer as a result.
The first rule is very simple – you must be 13 to get any form of paid job in the UK. Once you reach 13 there is a list of jobs that you can do, and these include things like a paper round, shop jobs like till work or shelf stacking and café / restaurant work like serving food and clearing tables. A full list is available so make sure you check it out, but those are the three most common things that you are likely to be able to find a job doing.
As you get older the type of work that you can do increases, but you need to keep an eye on the regulations as some jobs are prohibited no matter what age you are. These jobs tend to exclude anyone of statutory school age, and include delivering milk and working in adult type premises where age limits apply, for example a betting shop or a licensed bar. However, you could work in a licensed bar when it is shut, for example, you could clean there.