Dark Water hinted that the Master/Mistress's TARDIS was disguised as a phone-box outside St Paul's Cathedral ( wouldn't it be impressive if St Paul's itself was the form it had actually chosen to blend in with its environment?). Oh, the joys of a working chameleon circuit! What better excuse, then, to have a look at the various forms its taken over the course of his/her various incarnations? One of its first assignments occurs in The Dark Path- before the Master had even become the Master. Here, he's known as Koschei & is actually working for the Time Lords on the Darkheart alongside a Celestial Intervention Agent companion, Ailla. He believes her to be human- but his employers are actually using her as a spy, wary of his interest in things he shouldn't meddle with! The Second Doctor believes him to have been sent to capture him, in a foreshadowing of The War Games.......
Koschei's Type 45 TARDIS is implied to take the forms of a flyer for the Adjudication, the lawmen of Earth colonies, & then an out of date locker. Hints at the man he will become abound- he uses hypnosis on Victoria Waterfield & seeks to use the power of the Darkheart itself for his own destructive ends. What sends him over the edge? Ailla's implied death- her 'betrayal' enough to eliminate any trace of good in him, which explains why he is as he is upon arrival on Earth to test the Third Doctor's patience! In his ( Roger Delgado's) first screen appearance in Terror Of The Autons his handy temporal transport has taken the form of a horse-box to blend in with its surroundings at Luigi Rossini's circus.
By The Claws Of Axos its a simple white cube. Colony In Space sees it posing as a spaceship while its pilot impersonates an Adjudicator. & by the time of The Time Monster it's a computer bank in line with the Master's guise as Professor Thascalos, while he works on the TOMTIT- Transmissions Of Matter Through Interstitial Time- machine in a bid to get his hands on the power of Kronos. During the events of The Face Of The Enemy- possibly the only novel in which the Master appears as the main character- what looks like a Rolls-Royce limousine is actually his TARDIS, which will also change into a bulkhead door on board HMS Redoubt. It'll be a BBC outside broadcast van by Harvest Of Time….
Next up is an approximation of a statue of the Melkur in The Keeper Of Traken. Before it's destroyed it's shown to be able to walk & fire lasers from its eyes! After it's dispatched, though, a handily ready to go second TARDIS takes on the form of a grandfather clock, from which the dying Master ( Peter Pratt) emerges & latches onto Tremas, giving himself a new body. The ' corpse Master' will also adopt a tank-TARDIS in The Light At The End.
In Logopolis it takes on an outer shell more commonly attributed to his equal & foe's Type 40 as well as that of a Doric column- think along the lines of classical Greek architecture.
It'll do the same in Castrovalva & Time-Flight - judging by the number of times this form is used, we might presume it was the second Master ( Anthony Ainley's) choice of default exterior appearance!
In between those it will also become a marble fireplace & a Concorde plane! 'Sir Giles Estram's adopts the guise of an iron maiden torture device in keeping with the period setting of The King's Demons. By Planet Of Fire its reverted to a simple three-sided column, while in The Mark Of The Rani.........he hitches a lift with her.
When he pops up at the Sixth Doctor's court date in The Trial Of A Time Lord he does so in what looks like a beach hut followed by a statue of Queen Victoria. Having regenerated once more, his snake-form guides the Doctor's TARDIS to a fateful encounter in 1999. The novel The Eight Doctors suggests that he had sent his own TARDIS to the Time Vortex to await his arrival, & when he retrieves it following the failure of his final trap for the Eighth Doctor he's left it in the church at Devil's End. An incarnation portrayed by Alex Macqueen disguises his as a telephone box in Eyes Of The Master, too.
Of course, following his regeneration/resurrection, he simply steals the Doctor's own TARDIS to travel into the past, turning it into a 'paradox machine' to stop the Toclafane's killing of their own ancestors affecting the flow of time! Which leads nicely to that red phone box/ St Paul's in Dark Water.................