Well the Japanese invaded British colonies on the very same day as Pearl Harbour (it appears to be on a different date because of the date line). British, Australian and other colonial troops fought extensively in New Guinea, Malaya and Burma to defend the (British) Empire, and many were imprisoned in horrific conditions by the Japanese and died in PoW camps due to starvation or forced labour or were simply executed.
Source: High School in Australia.
If you're counting the British Dominions as part of the UK, Australia and NZ troops were heavily involved in the land campaign in Indonesia and Papua New Guinea. It was Australian troops who first managed to stop the Japanese land advance across PNG, and both Australian and NZ troops were part of the Solomon Islands campaign.
The British were also the prime movers in expelling the Japanese from Burma.
Stalin promised (at Yalta iirc) to open a front in the east within 3 months after Germany's surrender. A few days before this deadline, the USSR indeed started a campaign into Japanese-occupied Manchuria. This offensive was largely succesful, but it was cut short after Japan's surrender later in that year.
(I'm on my phone, so I don't have any sources at hand, will add some if requested.)