You don’t apply for a permit, you go to LinesearchbeforeUdig - lsbud.co.uk. This is a free service anyone can use, and you’ll get emails from various asset owners with maps of what they have in the area you select. Some might try to charge for this, these ones are assholes.

As far as the law is concerned, it’s up to you to make sure you do it right and the costs for doing it wrong will all fall on your shoulders.

The only permit you need AFAIK is planning permission - which won’t be granted until you convince them you’ve done a sufficient line search. Aside from that, you need permission from the land owner, of course.