At the time the Congo was unexplored. The British only knew that it was big, so they didn't want a powerful nation to take over it in case it turned out to be rich as well (which it indeed was in the end). Yet they didn't want to take it for themselves because they didn't knew for sure if it was worth it.
At first the only counter-claim to the Portuguese claim was the French one and the British certainly didn't want the French to take the whole Congo, so they supported the Portuguese. When Leopold II stepped in, the British supported him because Belgium was even weaker and more dependant of British support than Portugal. Moreover, Leopold's project was presented as turning the Congo into a de facto independent state with only loose ties to Belgium, which was something even more attractive to the British perspective of "the weaker, the better".