I think OP is reasonable in her assumption to a large degree because if, in a park, a person were taking photos of children playing on play equipment, and a parent challenged them and made a fuss, I think that a community police officer or park warden, would, indeed ask them to stop doing it. Ditto, in a street, or at an ice rink. If the photographer said they were doing it to supply inspiration for an art project they were doing, the 'official' would still tell them to stop.
Although not illegal yet, I think it soon will be made so. Swimming pools won't let bathers be photographed. I think soon parks may advise members of the public not to take snaps of children playing. I don't know who would be the enforcing body ( as in, swimming pool management, for a pool), perhaps the organisation which runs the park; perhaps the council; perhaps the police.
The salient issue, I think, is that young kids of six or so, play un- self-consciously and might have their skirt riding up, if a girl, and not be aware enough to cover themselves. It's very intrusive and inappropriate to photograph children, for this reason, especially.
If someone posted on a neighbourhood forum an image they had captured - a shot of a man with a camera taking pics from the edge of a play park, then other posters would reply how awful this is and well done on that OP for telling him to stop. Nobody would think it were ok. I guess, also, that new school are now often constructed with tall sides to the buildings with windows you can't look into, in part anyway, to stop perverted onlookers gazing at teenagers in uniform.
I'm sure taking photos of other people's kids in public will soon be banned.