It's private land, so they can *eject* but even the UK police can't seize films / destroy photos / remove your property without going through an awful lot of paperwork (if at all). Hell, be too rough when ejecting them or damage that property even in a minor way and you'll be before the court, not them. The police can't even ask YOU to delete the images, technically.
I can put up "No filming" signs in my street. Poke the camera into my house and you have a privacy violation and I can call the police who may well arrest you (sign or not) but I can't take that equipment from you (necessarily). Film unobtrusively and without invading my privacy and neither I nor the Police can do anything without arresting you first (and then you have to prove they did something illegal, like here, which is very difficult).
If I own a nightclub, with a "no-filming" rule, I can ask you to leave if you film. I can call the police if you've been filming up girl's skirts. But *I*, nor anyone but the police, can legally seize your camera or make you delete the photos except in order to detain you until the police arrive (and if you *haven't* technically committed a crime, that could be seen as unlawful imprisonment).
Basically, nobody is allowed to touch someone else's personal property (or person, technically) except in the process of arrest (possibly "citizen's arrest") on suspicion of a crime. You can't just put a sign up and make your own private laws. You can eject, if you do it within the agreed legal parameters. You can ask for them to be arrested. If it's serious enough, you can "arrest" them and call the police who will probably end up having to let them go anyway.
But you *can't* seize their camera, make them switch it off, switch it off for them or get them to delete photos. You can only refuse entry to people with cameras and / or eject people from the property if they use cameras against your "rules". In this case, the airport was classed as public property and, as long as there wasn't a *genuine* security reason, the airport was deemed wrong in demanding that they guy turn off the camera. It's also *NOT* illegal to film your child's school play, no matter who's in the photo, but you *could* be ejected from the school (there is a quote from a senior ministry about stopping such "nonsense rumours" going around - it's not illegal, it's just a per-school rule that makes people THINK it is illegal). It's not even illegal to film in a public street whether you ask people's permission or not. But it's considered polite.
The law is surprisingly liberal in this area. Whenever someone comes to you claiming 1984 is occurring, have a look at what a private citizen is *allowed* to do. You might still be harassed by police but the last few times they got the law wrong on the street, photographers held a protest in London and the police chief had to send around "guidance" to police officers across the country.