There is no law keeping you from photographing anything if it is in or on a public space. At least in the US anyway. However, I would guarantee you a visit from the local policeman if you were to start photographing children on a school playground for instance. You would probably get a request to leave.
The problem comes when a person has an expectation of privacy. No matter where they are for instance in a public restroom. I suspect the UK has similar laws but you need to check.
In a word, photographing other people's children is not a good, or perhaps healthy, idea without the parents permission.
EB
EOS 1DX and many lenses.
