Hello, Dolly!

"Hello, Dolly!" was a song that the Fourth Doctor once sang to divert a Pescaton rampaging through the streets of London. He accompanied the performance with dancing. The overall performance was more successful at temporarily taming the beast than had been several other more aggressive options. (BBCR: Doctor Who and the Pescatons)

Behind the scenes
Tom Baker does actually sing the first few bars on the audio. At the time of the audio's release, it was the first time that the Fourth Doctor had been heard to sing in a piece of performed Doctor Who fiction.