Not an area of huge British activity. We seem to have built trading posts in the territory in 1663, but the Dutch objected and rapidly destroyed them.
Unsurprisingly, though, armed British ships have spent some time in action in Liberian waters. For example, in 1721 the Welsh (or British) pirate Bartholomew Roberts captured the frigate Onslow at Cestos Point, on the River Cess in Liberia. And in the nineteenth century, British anti-slaving patrols operated in the waters of present-day Liberia.
In the 1820s, the American Colonization Society began sending to the area freed slaves from America, a move that created the foundations of the state of Liberia. Shortly after that the new Liberian government tried to impose duties on goods imported into its territory. We didn’t like this too much so we seized the revenue schooner John Seyes at Edina, in Liberia, and confiscated it.