Unless the camera is being used in some criminal manner, such as voyeurism, or breach of certain terrorism regs, the use of cameras in a public place is an entirely civil matter, and ACPO (now the NPCC) expressly forbid officers from becoming involved in civil disputes beyond the requirement to maintain the Queen's peace.
Just to add to
@Drago of the Yard's post, these days you do need to be a bit more aware of your rights when in a 'pseudo-public' space - shopping developments typically, but you'd be surprised how often you step off public land without realising.
Although at first glance they're open access just like a proper public space, you're there on the sufferance of the landowners and they do have the right to ask you to stop filming or photographing or leave the premises. They certainly can't seize or inspect your equipment, or force you to delete anything. You can usually spot these places because they have some minimum wage security droids dressed up as policemen hanging around.
In a public space there are few restrictions on what you can film away from anything covered by the official secrets act or other security legislation. There's no law against you going to your local public park and taking pictures of the littles without their parents' permission. You'll likely get your head kicked in though, so I wouldn't recommend it.
I've had to get my head around this as I do the photography for Bolletta's skating club and also deal with some of their safeguarding. It is a minefield, but nobody's ooman rights are being infringed by filming in public.