Pudding was a type of dessert. It was sometimes also used as synonym for dessert.
The Fourth Doctor joked to Thawn that Kroll was saving him for pudding. (TV: The Power of Kroll)
In 1887, the Seventh Doctor, Sherlock Holmes and John Watson once consumed a pudding made from boiled rice and coconut flavoured with rose essence. (PROSE: All-Consuming Fire)
Clara Oswald and the Twelfth Doctor had a dinner date in 1937 Berlin, which involved some pudding. (TV: Kill the Moon)
The Tenth Doctor thought that the word "tulgy" was very good for describing puddings, claiming that he'd had some wonderfully tulgy puddings in his time. (PROSE: The Nightmare of Black Island)
Angie Maitland asked Clara Oswald if her mum was deep on puddings. (TV: The Name of the Doctor)