Aged up to (and including) 13 years old you can be employed in certain types of job:
- sport, advertising, modelling, plays, films, television or other entertainment (employer requires special licence)
- odd jobs for a parent, relative or neighbour
- babysitting
- others covered in local by-laws (typical examples, paper round or milk round)
14-16 you can do pretty much any job provided it's one that is classed as 'light' work, so working in a coal-mine or factory is out. So too is working in a pub or bar as you're not allowed to work past 10pm. You're also not allowed do any job that is likely to be harmful to your safety, health, development, or that will affect your attendance at school.
So if you're over 14 you could work in an office, you could work as a shop assistant, you could work in catering (but not in the kitchen), you could work in a hotel, in fact you can do pretty much anything so long as it doesn't interfere with school hours, specifically not more that 2 hours work on a school day. Leaving the weekends and school holidays as your big earning times.
And you're lucky in that the law protects your breaks, 13-16 year olds get a one hour break every four hours and the most they can work is 8 hours a day (5 hours if under 15). We adults don't get that.
16-18 you're then entitled to the 'minimum wage' and as a 'young worker' you can do pretty much anything, even join the Army if a parent or guardian agrees to it, and there can't be many professions as hazardous as one where you're paid to be shot at.