Wilfred "Wilf" Mott is the Rani.
He (she) killed the Doctor! What kind of moron is going to lock himself inside a cage while there's a Time Lord battle royale going on? Like the Fourth Doctor used to do, Wilf (The Rani) was just playing the fool in a diabolical scheme to make the Doctor take his own life. The Doctor found it very odd that he and Wilf kept meeting each other over and over. This was no mistake. The Rani (Wilf) has been carefully stalking the Doctor for years, waiting for her opportunity to take revenge.
But isn't the Rani a woman, you might be asking? Maybe. Remember, the Rani is a master of disguise. Her spot-on imitation of the Doctor's companion Mel managed to fool the Doctor. Therefore, playing an old man the Doctor wasn't already familiar with would be easy. Alternately, the the Rani may have been a man all along. Don't tell me Kate O'Mara doesn't sort of look like a man in drag.
She (he) killed the Doctor! It's been well-established throughout the series that other Timelords are no match for The Doctor. Instead, the Doctor is normally done in by his companion (9th Doctor), common street thugs (7th Doctor), or simple clumsiness (4th Doctor, 6th Doctor). The only exception to this rule is the trio of Time Lords who were somehow able to force the 2nd Doctor to regenerate. Maybe they were the Rani...