Once the extension is complete, would it BU to not allow the neighbour complaining to then use said new driveway for access to complete building work on their property (albeit smaller work)? Actually once the extension is built
Speaking from first hand experience... OP, once the rather large extension is built, presuming that firstly you get planning permission(they do have a right to light in certain circumstances btw), and secondly, that you’re perfectly OK with permanently upsetting your neighbours, for possibly the entire duration of you both living next door to each other. That could literally be decades!
Especially as the disagreement will probably result in them
not talking to you and probably creating a really tangible awkward ‘atmosphere’ between you. Other neighbours may unintentionally become embroiled by the circumstances too and feel torn, with divided loyalties, speaking from experience... Inevitably, it would be seen by many, including your neighbours, as totally petty of you indeed to deny them access to complete their extension, having already completed on your own extension. Denying them access to complete their own extension may detrimentally affect the final finish of it, which may become an eyesore for you as a result.
If either of you moved, or should I say ‘when’ as that’s inevitable at some point, then whoever is moving house would be legally obliged to declare the animosity, and how it arose, in a legal document, a really extensive multiple paged questionnaire about the property.
Personally, and I think many would agree with me, that it would be really very petty of you to deny them access to facilitate them to complete building works on their property. Especially given that, as you put it, they’re extension is “albeit smaller work”. If you don’t allow them access, then they maybe forced to complete the work for their extension from ’their’ side. Which could then have an impact upon the final finish of their extension, and become a permanent eyesore for you.