Pedestrians and cyclists do not mix, even in parks, unless the lanes are completely separate and not just a lined-off section of a walkway. Today in SE22 I saw two lots of magazinified parents - daddy up front with baby/toddler in a basket, mummy at the back and the other kid riding in between - on the pavement. Having a child cycle with you doesn't allow you to break the law. (They sped off too quickly before I could tell them.)