Declaration of interest: I work for a building materials supplier.

You're on the right track. Once the porch is enclosed, that old brick vent is no longer open to outside air, so Building Control are right to want a continuous path out to a new external vent on the side wall.

The awkward bit is matching free area rather than the face size of the airbrick. A standard brick vent looks about 215 x 65 mm on the face but the actual open area is much less, so size the duct to that free area and do not pinch it down at bends. A short horizontal run with one gentle 90 degree bend is fine.

In practice people use either rectangular flat channel duct (Domus / Manrose style) with adaptors onto the airbrick sleeves, or 110 mm soil pipe with square to round adaptors at each end. Both are easy to get from merchants. Keep a slight fall to the outside so any rain that gets in drains out, seal the joints so porch air does not leak into the underfloor void, and fit a proper airbrick or cowl at the new outlet rather than leaving a bare pipe end.

So yes, horizontal extension, flat 90, then out to a new brick vent is a normal detail, not a joke from the architect. Just keep the run short and the free area up.