This is true. I have a picture of Factory Workers parading in Leningrad and all are carrying early Lee Enfields.
There was lots of .303 British in Latvia, Lithuania, and Estonia all of whom were supplied in 1919 by the British to fight the Bolsheviks with Ross, Lee Enfields, and P14s, as well as Lewis guns and other machineguns.
The invasion of Archangelsk is another matter. I assume there may have been caches left over but with the proximity of Leningrad to the Baltics I would assume the rifles were from there.