Not impossible that a very large and very mature Jasmine officinale (assuming its 12 feet wide at the base and over 30 feet in height) MIGHT cause problems, but it's not very likely. It's trees which cause the main trouble - no tree should be within 40 feet of a house as an absolute minimum. Passiflora and honeysuckle, not a problem. You don't say what part of the country you're in, but if you're in the south, despite any rain we've had recently, there is currently, technically, a drought.

Thank you, The Jasmine in question is only 8 feet high and we keep it well trimmed so it has only spread about 12 feet.
We live in Northamptonshire.
It sould like I should remove the Jasmine to keep the peace.

Personally I'd leave the jasmine exactly where it is unless your neighbour can prove there is a problem - which I doubt as Bamboo says trees are the big problem.

Is the Jasmine growing up their house wall? Because if it is, that's technically illegal - if its growing up a support you've provided for it against a wall, that's fine. I certainly wouldn't remove it on the strength of a bit of soil shrinkage - your Jasmine is unlikely to be the cause.

The Jasmine is growing up a support we provided so I am in the clear.
Thank you once again

Perhaps your neighbour just needs to talk to his builders, regarding foundations in clay, which always cracks in dry periods?! Also, is there a tree, as bamboo suggests, that could be sucking out the moisture - willow, conifer, anything at all, on his side. Or perhaps there has been a drop in the water table in your area, generally? Again, if the builders did not allow for this they they are ultimately liable. There is no way that your jasmine could be undermining his property. Stick to your guns and ignore him.