You are confused about the rules and terminology.
"Permitted Development" is a planning reference and refers to an allowance whereby homeowners can build an extension of a certain size without seeking planning permission and has nothing to do with "Building Regulations".
Whilst you are correct in thinking connies are largely b'regs exempt they are not entirely exempt depending upon size and content.
There is evidence to suggest that work by association does mean that BC do tend to ignore work that goes on and around connies. I think you can safely say that a reduction in vent pipe bore size would be one of those they would not be interested in.
It also means that (unfortunately) conny companies can do as they wish.
I don't seriously see this a problem worth worrying about.
Some blazé tradesmen see fit to plonk AAV's onto SVP's whenever they want to or just leave them out altogether. The fact that yours is venting is a boon. My only criticism is that the (reduced) pipe bore could have been larger, but no great crime.
Why on earth would you go to all the hassle of making that image BAS? Just to make a point on a thread that will end up in the quagmire and forgotten about for ever in a few days anyway?
If you burnt every book you read when you learned its contents, how would the person who comes after you, hoping to learn from the same books, learn anything?
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