The earlier declaration by the UK was due to the Japanese attacks on the British colonies of Malaya, Singapore, and Hong Kong, and also due to the fact that the British did not have the American constitutional tradition of requiring the consent of its own national legislature to declare war - the British cabinet could declare war without consulting Parliament, and therefore could act more quickly.
The UK's earlier assertion was triggered by Japanese attacks on British territories in Malaya, Singapore, and Hong Kong, and also due to the absence of a constitutional requirement for British legislative approval prior to going to war - this enabled the British cabinet to act more swiftly without consulting Parliament.