I'm afraid that it was also your mistake, (and also one which you won't make again, and hopefully one from which others will learn a useful lesson) to allow the work to commence without a full-plans approval from Building Control.That was my mistake and one I won't make again.
The Building Notice route does not cost any less, so there is no reward for taking it, but it does increase the risk. If plans showing 100mm had been submitted in advance, they would have been rejected, and the problem fixed before a single penny or day was spent on construction.
And infinite risk:reward ratio makes no sense whatsoever.