I found a reference from the Dozenal Society of Great Britain, and although they list sources they don't explain what particular source this information came from:

Peter the Great worked in English ship yards in 1697 while he was Czar, and made the English foot standard for his country on his return (and that led to our adoption of the Petrograd Standard of softwood measure: 165 cubic feet, or 120 pieces 12′ x 11″ x 1-1/2″). The metric system was enforced in Russia after their revolution, perhaps for the French reason, 'pour changer tout cela'.

Peter the Great's stay in Britain lasted for about four months (he wasn't actually working in the shipyard, but studying shipbuilding (1), which I suppose is a very insignificant difference).

Presumably the reason the Soviets stuck to English calibres was simply a matter of inertia in their industry; rather than rechambering everything and changing all their tooling, they simply re-numbered the English calibres in metric units and went along with their business.

(1) Royal Museums Greenwich