Bednobs answer might be correct 'in practice' but it's certainly wrong 'in law'. If, say, the owner of a corner shop permits their child (under 13 years old) to assist in the running of the shop (whether paid or unpaid), they're breaking the law.
It's illegal for anyone to employ a young person under 13 years of age. (As Saxy_Jag has indicated, local authorities may have bye-laws which prohibit 13 year olds from some forms of employment).
There are lots of rules associated with the employment of young people. For example, the employer has to notify the local education authority. The LEA will then, if appropriate, issue a permit. This can be withdrawn if the pupil's school work appears to be suffering or if they have other concerns (e.g. over safety).
There are lots more rules which, for example, state the maximum number of hours which can be worked and also the times of day when a younfg person can be employed. Full details are here:
http://www.direct.gov.uk/Parents/FamilyIssuesA ndTheLaw/ChildrensRights/ChildrensRightsArticl es/fs/en?CONTENT_ID=4002945&chk=AaZA0p
Chris