Birmingham Proof marks on a "London" gun can mean two things,
1, it was made by another maker and sold out of Cogswell's shop as their own ,this was common practice and contiued up to the 70s,to my certain knowlage.
2,it might have been rebarreled ,are there London and Birmingham marks on the action flats?
As to the chamber lengths almost certainly been 2&1/2 inch roll turnover ,which would mean very little chamber cone,so pleaase dont use longer cases.