Factual error: The story "The War Machines" is (probably) set in London in July 1966. At the time, England, and more specifically London, was hosting the F.I.F.A. World Cup Soccer Tournament. But you wouldn't know it from watching this Doctor Who story... Sir Charles Summers mentions July 12th (1966), which was the day after England played Uruguay at Wembley and the day before Mexico played France. The other matches involving those four were played in London during the time the events of "The War Machines" are supposed to take place, but no mention is made of the fact, there are no foreign football supporters roaming the streets and no flags or posters on display. Did the story take place in an "alternate reality" London of July 1966?
Factual error: This story is set in London in 1966 - the Post Office Tower was completed in October 1965). July 12th 1966 was a Saturday, not a Monday.
Plot hole: It is highly unlikely that the discovery of a dead down-and-out's body in an empty warehouse would be reported in a national newspaper, especially as the discovery had to have been made when the newspapers were already being printed.
Answer: TARDISes are generally available for properly authorised use on Gallifrey; they're not usually assigned to a particular Timelord on a long-term basis. The Doctor stole his when he left his homeworld.
Tailkinker ★