If BC pass it, then probably it is what it is - the builder can carry on, and the BC confirmation would put him in a very strong position to demonstrate reasonable skill and care should you ever try and sue for negligence.
However, if BC don't pass it, they may or may not give any recommendations. My understanding is that since the building safety act BC are avoiding any design liability whatsoever. You need to think very carefully about the contractual relationship, which is between you and the builder. I would put a stop on the work until the builder produces his SE's calculations. Point out to the builder that should there be a failure, you will be claiming against the builder (as that's your only contractual relationship) and hope he has professional indemnity insurance (as he is involved with the design of the building having insisted that he won't use your design), and if he doesn't have any he may be in deep poo. Of course, the builder will (?) have a contractual relationship with the SE, so if you sue him, he might sue them. A lawyer fest.
I have personal experience of design liability and PI. A company I worked for bought in a component from an EU supplier, that our customer actually approved, but it failed because of a design fault. The end user (customers' customer) sued our customer, our customer sued us, our PI paid out ( as we demonstrated we used RSC and hence it was an insurable event) and then our insurance company who paid out sued the EU supplier. Whether they succeeded I know not.