The "Tower" (of London) was at that time was the Headquarters of the Board of Ordnance as well as the major repository of arms for the British service. Guns were not actually made there. The practice, in an effort to improve interchangeability, was to have parts made by contractors, who then brought the parts in an unfinished state to the Tower where, if they were found acceptable, they were marked with acceptance stamps or engraved markings, and fitted and assembled by Tower (government) workers into complete guns.
The crown on those lockplates, as well as the word "Tower" were hand engraved. (Later, after about 1809, they were stamped, but that is beside the point here.)
The markings on that gun appear to be hand engraved, and the age seems right for an original. In short, it may have some discrepancies, but none are obvious to me.
Jim