Hello and welcome to the community.
First, if you can go back to that Tony Soper program and see if it gives a date that the nest was removed and any other information as to why, also, when was that program first broadcast, look for the copyright date at the end of the closing credits, it may be before the Wildlife and Countryside Act 1981, so a lot that was carried out then, could be illegal today.
Also, Tony Soper was a naturalist, and quite prominent in his day, and may have permissions to undertake some activities that would be illegal to us, but as I already mentioned, the law has changed somewhat.
If I'm wrong, then someone will quickly chip in and correct me, but as I see it, there's nothing you can do, as nesting sites need to be left undisturbed, but I'm more than happy to be corrected in this instance.
The link to the Wildlife and Countryside Act 1981 is: https://www.legislation.gov.uk/ukpga/1981/69
Mike
Flickr: Peak Rambler
You're welcome Paul.
While i understand why you're putting blankets under the nestbox, please ensure it doesn't have loose manmade fibres, which I fully appreciate is going to be difficult these days.
And only do so if there's no risk of disturbing the nesting great tits.