As Lore's link indicates there is no actual age specified. However, a young person must be 16 years old before they can take on temporary legal responsibility for the welfare of a child. (If a younger person is allowed to babysit, the parents/guardians remain legally responsible for the welfare of the child).
In practice, some commonsense has to be applied. A parent might quite reasonably leave the house for just a few minutes and ask their sensible 10-year-old child to keep an eye his/her baby brother/sister for those few minutes. This is obviously completely different to going out for a 'night on the town' and expecting the same 10-year-old to take charge.
14 is often considered to be the youngest age at which a teenager should be asked to babysit but some 14-year-olds are far more mature and responsible than others, so some discretion is required.
It's also worth remembering that it's illegal for anyone (including parents) to employ any school-age child (whether paid or unpaid) in any occupation (including babysitting) after 7.00pm. on any day (including weekends and school holidays). On school days, and Sundays, the total time worked must not exceed 2 hours. (There are addition regulations but those are the main ones which are likely to apply to babysitting).
Chris