Britain's war with Finland produced little naval action

Did the Royal Navy operate against Finnish ships after Britain declared war on Finland in December 1941?

Not to any meaningful extent; Britain was formally at war with Finland but conducted little naval action against it.

Formal belligerency did not lead Britain to conduct meaningful naval operations against Finnish ships in support of the Soviet Union. The Royal Navy saw little action in that theatre. A declaration of war does not by itself indicate the scale or form of actual military operations.