The United Kingdom is not at war with Russia, so the two countries are not enemies in the legal sense.
However, it is an offence under the Foreign Enlistment Act 1870 for any British subject to serve:
in the military or naval service of any foreign state at war with any foreign state at peace with Her Majesty
(From section 4 of the Act.)
This issue was raised with respect to British volunteers who went to fight with the Ukrainian army, as in theory they were breaking the law. Therefore, we can surmise that anyone who left to fight with the Russian army would also be acting illegally.
However, as the linked article mentions, prosecutions under this Act (or its 1819 predecessor) are extremely rare.