Neighbours drain blocked and is asking us to pay

ThisIsWeird

DEd, please don't overthink this, and definitely don't get drawn in to any 'discussion' with this neighbour. Stick to the essential facts as they are known, and repeat them. You do not need to answer every weird 'what if' from this neighb or anyone.
Folk like that have a way of twisting and dragging arguments down all sorts of convoluted paths, are extremely unlikely to listen to reason, and even less likely to conclude, "Ah, I see! Yes, you are right - it has nothing to do with you!" They only want one thing - the outcome that they are after, at anyone's expense. In this situation, he hasn't a chance. So don't let it become fraught. Just ask ask ask - they need evidence evidence evidence.
Stick to some simple lines, and try and end them with a Q. 

"You do know a Buddleia in itself isn't going to damage a drain that is in good condition, don't you?!" Nail them down on this by repeating it ad nauseam until they are forced to answer; "You KNOW this, don't you?!"

If they actually try and claim that your particular Buddleia was armed with a jackhammer, then turn the onus on to them to prove it; "You'll be able to provide evidence for this, won't you? You don't just expect me to take your word for it, do you!"

"What came first - the damage to your drain, or roots getting in? Uh-huh. What came FIRST?!" Repeat repeat repeat.
"You do know that YOU had a large conifer growing near your drain, don't you?  Now, that could have moved the drains causing damage to them, so how come you aren't blaming your own tree - which is an actual possibility, when everything else is not?!"

"If you really think you have a case, then get on with it."

Since they have shown that they are silly and/or devious, and can become tetchy with it, then something else that could be very useful is a discrete recorder for all future conversations. Either have your phone set to do this and have it in your pocket, or buy a 'pen' style unit for less than £20 - they work really well. If the guy is daft enough to try and escalate this, you can show your complete calmness and reasonableness, and their rantings. If you do this, don't share any of it - keep it simply for if a 'case' arises.

D_Edwards

A Buddleia armed with a jackhammer! That made me laugh! Thank you. We are now definitely not paying anything to him and he has no right to demand any money from us. I believe we will no longer be on good terms going forward but this has shown us his true nature. 

Now might be a good time to tell him to remove his metal gate latch that’s attached to our house as it loudly rattles through the house every time he goes through it!!

breaking_free

In your position (though others may disagree) I would share this thread with him so he can read other people's takes on this situation. I once did this myself and the person disagreeing with me, after reading other people's views, reluctantly accepted that I was being reasonable after all.