In what story did the gag of the Doctor having bottomless pockets originate?

The earliest suggestion that The Doctor had 'bottomless' pockets was in the Second Doctor story The Space Pirates, in which he firstly pulls a pair of magnets on strings from them to demonstrate magnetism to Jamie. Later on, he produces a pack of drawing pins from his pockets, to which Zoe remarks "what are you carrying drawing pins for?". Later still, he fumbles in his pockets and produces a tuning fork which he uses to pick an 'audio lock'. That The Doctor should be shown to carry such a bizarre array of items in his pockets in the same story, all of which he just happened to need, seems to be the beginnings of this trope. The Second Doctor also produced sticky tape, a pair of scissors and some silver wire from his pockets in The War Games.

To the best of my knowledge, there are no such instances during the Third Doctor's run. However, the Fourth Doctor showed that he was carrying a large assortment of items from his pockets in his very first story Robot, in which he was shown to be carrying a fake pigeon, a yo-yo, jelly babies, a scroll from Skaro, a pilot's licence, a galactic passport, and honorary membership of the Alpha Centauran Table Tennis Club.

The first time the size of his pockets was formally acknowledged and explained was in Runaway Bride when the Tenth Doctor said they were "bigger on the inside".