How this works in the UK normally is when you're knee deep in the purchase process you have to get legal searches and a survey and the lawyers or surveyor will find the tunnels have no permissions and then you will not be able to borrow money to buy the property because no bank will lend when there is an adverse survey or there are legal questions associated.

You can get these types of things sorted (eg apply for retroactive planning permission) and the council will send a surveyor and give you an opinion but you are running the risk that they insist you either make it good (remedy anything they don't think was done right) or (worst case scenario) tell you to put it back like it was before the unpermitted work was done. This happens more often than people think.

That's why the house has been reduced in price so much - to find someone who feels like the headache is worth it. I have my doubts to be honest.

And if they were permitted you'd still have the liability. It's not like the permitting authority is gonna say "aw well we let you do it this is on us" if something happens.

"Real" liability of the "if something happens I'm on the hook" kind is not what's driving down the value here. What's driving down the value is that now that there's a bunch of pictures floating around the internet the tunnels are worthless because some government inspector could choose on a whim to force you to fill them in at your expense (which you would presumably fight, expensively, in court).