Players does feature Churchill meeting both the Second and Sixth Doctors, but neither let him in the TARDIS (hell, the Second doesn't even have access to his TARDIS). For that matter, the Doctor doesn't even explain who exactly he is to Churchill. I'd explain more, but it would involve spoilers. And those interested can read it themselves, especially now that it's part of the reprint collection for the 50th anniversary.
That's why I think it must be in Shadow of the Glass if he ever does get inside the TARDIS, but all I recall clearly from that, Churchill-wise, is him arranging for SOE to parachute the 6th Doctor and the Brig into Germany so they can get a sample of Hitler's DNA...