Why Britain did not have to invade Singapore in 1945

Did Britain invade Singapore before the end of the Second World War?

No; Britain prepared an invasion, but Japan surrendered before it was launched, allowing the assembled forces to reoccupy Singapore quickly.

Britain had an unexecuted invasion plan before the rapid post-surrender reoccupation. Forces and shipping were already concentrated for an assault on Singapore. When Japan capitulated, those prepared forces could move directly into the port without fighting their way ashore. The speed of the return therefore reflected prior operational preparation rather than the absence of a British plan.