I think the simplest explanation is the likeliest:
The "Belgian barrel" may have been misdirection. To my knowledge European proofhouses did and do not proof handgun components as such. The Belgian proofs were applied when the gun was whole, or when the barrel was attached to another gun, but that's unlikely.
Both the Birmingham proofs and the Belgian proofs are blued over; the gun was refinished at some point, so we have no way to establish where it was proofed first. This was more likely a Birmingham conversion by a gunmaker other than P-H that was later exported to Belgium than the reverse, which would be carrying coals to Newcastle.
And back in the 1950s or '60s, when this happened, Britain was not a C.I.P. member state, so there would have been no reciprocal recognition of proofs.