Despite what has been said, it isn't strictly illegal to park across someones driveway... Look at rule 243 in the highway code, the rule commonly used to argue against parking across a driveway, it's a DO NOT rule, thus it isn't backed up by any law at all. It's not strictly illegal, but you can be given fined for it. Traffic wardens don't tend to do it too much though. Police might issue an FPN, though I suspect that unless you've got a garage, or if there's a car on your drive being blocked, they wont bother.
This goes for your own car as well (when you get one), you shouldn't park across your own driveway for a period of time unless you've confirmed your residency and vehicle details with your local council as you can still be issued a ticket.
The only time it is illegal is if you're preventing the owner of the vehicle on the drive (regardless of whether they're supposed to be parking on that drive or not) from accessing the public highway. If they're not preventing someone from accessing the public highway, it's a civil matter.
Either way, speak with your neighbour, if that doesn't sort things you can make a complaint to the local council. If one of your visitors are blocked in by them, again, speak with the neighbour, if they refuse to move it (or aren't in) call 101. Might not get it moved, but if police are there before it's moved they'll likely issue an FPN.