don't know if this is relevant but my daughter (14) is doing working experience at a Dog Rehoming Centre in March and she has been told that as she is not 16 she will not be allowed to walk the dogs unsupervised, don't know if this is for their insurance purposes or due to the law.
There is no legal age requirement, but if a dog is owned by a person under 16 then the head of the household is deemed as being the person responsible should there be any incident which could lead to prosecution.
I would think it is common sense to not allow a child to walk a dog unless you are confident they would be able to control it under any circumstances, such as being attacked by another dog or if the dog itself was aggressive to other dogs.