They can't, kids have to stay in education until they're 18 now
According to the government website they can actually leave school in June of the year they are 15, providing they'd be 16 by the time the next school year starts, i.e. somebody with a birthday in July can leave school aged 15. Elsewhere on the same site, people under 18 can work up to 40 hours.
Govt employment website says at 16 you have to be in paid work, self employed, an apprentice, in training or in education or a mix of these. What you can't be is an old school doley (neets). At age 16, they have to be paid through PAYE and officially enrolled on the staff payroll if they earn over £111 per week.
They must do 'some' part time education or training (which can be on the job CDP), up until their 17th birthday. That's how the army can recruit 16 year olds, a parental consent and a bit of on the job training with a certificate at the end of it and you're in.
So you could, in a very tenuous theoretical life, be a married member of the army, with a kid, doing 30mph up the High Street on your scooter, on the PAYE payroll - but not considered old enough or mature enough to vote in the local council elections.
I appreciate there aren't many in that demographic.