Most problems for photographers in the UK occur when taking candid shots of children.
It is perfectly legal to do so at present in the UK (and rightly so in my opinion) yet most parents dont agree nor see this as being right. It only takes one parent to report you taking photos of kids on a swingset before you end up with a policeman asking you rather pointed questions about your reasons for being there.
IIRC there is a leaflet available on the internet that you can print out and details all the rights of a photographer in the UK. Clarifies the subjects right to a copy of a print, details how permission does not need to be used unless its to be used in a defamatory or commercial sense... things like that. Have a google for "photographers rights UK" 
It isnt so much parents but teachers. I was up at St Marys lighthouse last year, taking photos of the buildings and a couple of teachers decided to try and question my use of the camera, even though I had the lens cap on, it was switched off and the camera was in its cover. The first was pleasant enough but I nearly told the second to FO.
Most other instances seem to be FUD involving things like transport, trains, buses, stations.
Teachers have a legal care of duty to the children and that includes stopping photographs of them being taken for non academic purposes (this has nothing to do with the law but a general LEA policy in the vast majority of places). Of course youd expect teachers to engage their brains and use a bit of common sense and discretion but unfortunately over half of the teachers Ive met thus far are hopelessly incompetent and would probably behave in the way that you describe.
That said I used to do a lot of work with kids at summer festivals over the summer when I was at uni for the arts and culture department of a certain Scottish council that shall remain nameless, I was told under no circumstances were any pictures of children to be taken by anyone, even their own parents, or it was my job. So at the end of the day I had nothing to do but stick he rule and ask parents to put their cameras away or save the photographs for elsewhere when they could be sure of not including other kids in the picture. You can imagine how hard that was to try and enforce this when organising something like a group of face painting for 50 kids all with parents in tow, all of whom wanted a picture of their beloved little terror with his or her face painted like whatever the flavour of the month was at the time.
I think its 99.9% bollocks myself personally, a complete overreaction and an extension of the paedophile witch-hunt. Wasnt there a case very recently where a school took down class photographs and suchlike from its website after parents complained or something daft like that?
Except that would totally exclude taking pictures of kids inside the school for purposes like selling the prints to the parents. How do you assess academic and non-academic purposes? A parent can take pictures of a play that can be entirely used by the performers in an academic way, examining how they acted, where they made mistakes, facial expression.
Thinking off the top of my head, if a paedo really wanted pictures of dressed kids they would have to go no further than clothing adverts, mail order catalogues and similar. Then there is the secondary issue of what happens outside school? Dance groups and sporting activities? Unfortunately you cant protect kids forever or completely, you can only do your best - and impose swinging penalties on those who actually do seriously breach the law. This also means keeping kids informed as to the law, what they should not be doing, what other people shouldnt do and when they should tell.
