Hello, I am a solicitor with over 15 years experience. I will try to help you with this.
Do yo agree that you bamboo roots have damaged his path?
I really don't know as he has taken up the two stones he claims the roots or root was growing up through.
Ok. if the bamboo on your property has grown into his property and caused damage then you can be liable to compensate him for that damage as long as it was reasonably foreseeable. Damage caused by roots can be, and often is claimed successfully.
As far as the light is concerned I don't think that is a problem. Your neighbour has no right to light and he can take no action against yo over that. (I assume from you description that the bamboo could in now way be described as a hedge).
As far as the root damage is concerned he will need to prove on the balance of probabilities that the damage is caused by the bamboo and that the damage is as extensive as he says it is.
Why didn't he just knock on your door and talk to you in a nice neighbourly way?
He spoke to Simon my partner on 14th September about the roots saying he had had to take up a stone flag and re-lay it due to the bamboo roots. Simon said we had had the same problem and been told the cut the roots off as soon as possible ( by the garden centre in fact ). We have been looking into the best way of containing them since and had already decided to dig a ditch our side and put a Rhizome membrane down but the gardener can't fit us in yet. We had no idea they had taken up more stone flags or had problems with any more. It was a huge shock today and a very unpleasant one.
I bet. You should definitely take the steps you are proposing and as soon as you reasonably can. As far as compensating him for relaying the slabs if he can prove the damage was caused by the bamboo then in law he will be able to seek and probably get compensation from you and your partner. He would need to issue proceedings in the small claims court to do this. You will know better than I whether he is actually likely to go to that effort over what I guess is no more than £200 or so. Whether you want to call his bluff or pay for/contribute to the cost of relaying is a matter for you.