Unless you're using an awful lot of water I'd be surprised if you are the problem

why not go round and have a look if there is a manhole in his garden lift the lid and have a look to satisfy your own curiosity.it could be blocked up from further down the drain and trying to lay the blame on you so you have to pay to get it blasted out.good luck.

I think you would have this in your garden too if it was down to you, more likely to be your neighbours problem.
But first when did you lay your concrete patio as it could be run off? but that sounds unlikely, more likely a damaged/blocked drain as its black and foul. Has there been any work done in the gardens or even on the buildings that could have damaged drains?
You can inspect your own drains first and if they are clear suggest your neighbour looks at his. Keep good records of anything you do do with photos where applicable.

If the water is black and foul smelling it could be drains related. Do you know if your drianage goes to a septic tank or to the public sewer?
If to a septic tank is the tank and/or soakaway on your own property or in the neighbours garden? If it is all conained in your own garden then the neighbours problem is unlikely to be anything to do with you; if in the neighbours garden then it is your responsibility.
If you are on mains drainage does a common drainage pipe run across your properties? This would suggest a choke which could be on your side or on his, depending on which way the drains run.
Why not suggest to the neighbour that you club together and get a plumber to come and inspect the problem and then take the plumbers advice. It shouldn't cost much and will save a fall-out between the two of you.

Thank you for all your answers so far, Unfortunatley it may not be possible to resolve the situation amicably as my neighbour is convinced it is me that is to blame and has sworn at me.

I will just have to prove that I am not to blame and your answers have confirmed what I already suspected.

My neighbour has put in a concrete barrier between his garden and mine to prevent water flowing into his garden & I suspect that in the process he has damaged his drainage pipe.

Why not contact your buildings insurance John they may well advise you how to proceed?

Sounds suspiciously like a sewer problem, possibly to be laid at the council's (?) feet--we would say "city services", here.

Doesn't work like that here, Tugbrethil. If the problem is in the home or garden then it is the homeowners responsibility. The council/water authority doen't take over until the pipe connects with the sewer in the street.