Do young workers have special rights under the Working Time Regulations?

Yes. The rights of young workers (those over the minimum school leaving age but under 18) differ in the following ways:

a limit of eight hours' working time a day and 40 hours a week
not to work between 10pm and 6am or between 11pm and 7am (except in certain circumstances)
12 hours' rest between each working day
two days' weekly rest and a 30-minute in-work rest break when working longer than four and a half hours.