A few things to consider:
1. Building Regulations
At the time the extension was built, it would've been subject to Building Regulations (if it was deemed habitable, and met other criteria... this may be something you should check).
2. Planning matters
References to the 4-year rule are correct. If I was the buyer/seller of the neighbouring property, I would keep quiet about the planning concerns and get the sale through. It may very well be the case that due to the size of the extension, planning was not required.
3. Rights to Light
Contrary to most replies so far, the estate agent is not talking rubbish. If the extension is causing sufficient 'injury' to the neighbouring property, under the Prescriptions Act 1832, then the neighbour could be due some compensation. The statute of limitations allows the neighbour to make a claim up to 6 years (perhaps 12?!) after the nuisance commenced.
Rights of Light assessments would have to be undertaken, and the whole process would greatly delay the sale if the neighbouring owner wanted to garner some free cash from your parents. The house could then be sold with a new covenant saying that the claim was settled and no new claim could be brought on the matter. This is worth looking into to make sure you have your bases covered. If you want any more steer on RofL, feel free to PM me.