I'm actually a Planning Enforcement Officer so it is literally my job to investigate these sort of things. Your local Council will likely have their own Enforcement team, or at the very least Planning Officers that undertake the enforcement side.

Your best bet (and to prevent any unnecessary delay) is emailing the Planning Department of your local Council with all the relevant information, including planning permission references and then it will be investigated accordingly, in this instance the breach being 'development not being built as per approved plans/permission'.

If a breach is found to have occurred then a variety of things could happen from the owners being asked to submit a retrospective application to an Enforcement Notice being served legally requesting they build as per the permission and remove any development without permission etc. otherwise they will be prosecuted. I can't comment on what this action would be as each Council has its own planning policies and each case is judged on its own merits etc

My Council keeps complainants details confidential but if you live next door then they will probably figure out it is you so bear that in mind.