The British troops did not really fight. The British landed in Murmansk with the explicit purpose to prevent the transfer of the allies military supplies previously provided to Russia from being seized by the Germans. In the beginning of 1918 the new communist government of Russia surrendered to Germany, and the Western part of the empire (if not the whole empire) fell into a complete disorder. There was a danger that the allies military supplies stored in Murmansk
may fall into German hands.
When in the fall 1918 Germany surrendered on the Western front, and the war ended,
the British forces withdrew. There was no real fighting between the British and the Communist government.
The British also had some limited involvement in Transcaucasian republics which
became independent for a short period after the 1917 revolution. They also
withdrew when Germany was defeated and WWI ended.
Another thing is that Britain supported the whites in the Russian civil war with supplies. This support was very limited, and did not include any British troups, only some technicians. A British tank captured from Denikin's troops
still stands on the main square of Kharkiv.
Somewhat similar was the story of American troops landed in the Far East. Their purpose was to prevent Japan from seizing Russian Far East.
Communist historians later called these things "foreign intervention". But there was no organized fighting between British or American troops and the Red army.