I've split my answer into 2 parts to get round the 2000 character limit. Here's the first bit:
There are two separate issues here. One is the age at which a young person is considered responsible enough to take care of a child (more about this below) and the other is employment legislation.
If we assume that the babysitter is employed to look after a young child then both national and local legislation is involved. Given that the most common occurrence when a parent uses the services of a babysitter is to allow the parent some free time in the evening then it is important to note that no school age child may be employed (even at weekends or school holidays) after 7.00p.m. On school days there is also a limit of 2 hours employment per day. Additionally no child under 13 years of age may be involved in any form of employment (with very few exceptions related to horticulture and agriculture) at any time. For more details check on your local education authority's web site. (The basic structure is shown on the Suffolk CC site at
http://www.suffolkcc.gov.uk/education/ews/parent_pt_jobs .html).
If the letter of the law is observed then no school age child should be involved in any form of employment (including babysitting) without previously obtaining a permit from the local education authority.
Even if a young person is not formally 'employed' to look after a younger child (e.g. if big sister is asked to look after little brother without payment) it's possible that the legislation referred to above may still be invoked. (As an analogy, it's illegal for someone who trades on a Sunday market to have his 15 year old son help him for more than 2 hours whether the son is paid or not. i.e. money doesn't have to change hands for employment law to take effect).
Chris