We are a Spanish couple planing a trip to London with our 9 yr old son next month. I assume there is a minimum age for which you need to have your own documents, but I am not sure what that might be, and can't seem to find it online.
I know you can travel using your national ID card, but in Spain you are not required to have one until you are 14 yr old.
Children do need some documentation in any case. In the past, children could also be included in their parents' passports but I think this is being phased out.
In fact, the requirements are often even more stringent for a child than for an adult because if the child does not appear to be yours (distinct surname), merely having a passport or ID card might not be enough. Similarly, in some countries, children leaving with only one of their parents might need an authorization from the other one.
