The photo of the barrel marks is not very clear, however, the 2 marks could either be Birmingham proof marks or private Tower of London proof marks. I cannot tell given the image. That the gun is labeled "London" is irrelevant because many Birmingham guns where marked "London" as a marketing device and many London makers used Birmingham barrels. All nonmilitary British guns that had proofed barrels will have 2 similar proof marks on the barrels. The first is the view mark, which is the original inspection of the barrel, and the second is the proof mark stamped after the barrel was fired with a proof charge. Generally, in Britain, gun barrels were made and proofed in Birmingham, or by the London gunmaker's guild (the proof marks with the crowns to which you refer), or you could pay the Tower to privately proof your barrels. The Gunmaker's guild marks were crowns over a "V" for view and then a crown over "GP" for proofing. They also had a crown over "F" for foreigners proof if you were not a guild member but you paid them to proof your barrel.