No, but they have to be doing something with a training/educational related element. So even if they get a full time job (unless it's an apprenticeship or a traineeship) they still have to engage in part time education or training.
www.gov.uk/know-when-you-can-leave-school
Worth noting that technically at 18 they can stop attending - but most stay until the end of the academic year. However, child benefit (if received) would still be payable to the parent until the first Monday so the YP can't claim UC until after this date.
The LA is supposed to follow up on those YP who are NEET, but whether their funding actually stretches this far is another debate all together!