Britain got sucked in because of their alliance with Belgium.
Screw the Belgians, look what they did in the Congo, they weren’t worth defending.
Britain wanted in. Any excuse would have sufficed.
The Belgian excuse was partly an “excuse” - the British gov didn’t care. They were more worried about the German empire being a treat to British trade.
Additional though, the British citizens felt sympathy for “the plucky Belgians”