Putin was given a plan to boost Russia's military by 30%, to 1.5 million personnel, the UK MOD said.
It is not clear when Russia would have these new troops and how it would get them, the UK MOD added.
Sweden and Russian neighbor Finland applied to join NATO in May, citing Russia's invasion of Ukraine, and are close to the end of the process.
Russia's army has struggled since its invasion of Ukraine, with widespread reports and intelligence updates highlighting poor training and low morale among its troops.
In September, Russia announced a partial mobilization of an additional 300,000 troops, which it said was completed in October.