Plot hole: Banning knows where there is an MI6 safe house but has "no option" but to head for the US Embassy. He could have gone for the Tower of London, Buckingham Palace, Knightsbridge Barracks, Downing Street, the Palace of Westminster or Scotland yard, all knee deep in security.
Suggested correction: The whole premise of not being able to go to the embassy is because they (the terrorists) will expect it. Banning also makes it clear to Asher that the entire security services are no longer to be trusted due to an insider. Going to any place "knee deep in security" is literally walking into a potential terrorist. The head of the UK response team even states they don't know who can be trusted and they need to eliminate the ones that have infiltrated the police forces. Hence the MI6 safe house.
Suggested correction: Considering the fact that there was a mole inside Scotland Yard, going there wasn't really an option.
Character mistake: When the Vice President has worked out Banning's signal he says "All right Manning" instead of Banning. (00:48:50)
Suggested correction: I hear him say "Banning."
Factual error: Air Force One has landed. The caption reads: "Stansted airport, 20 miles north of London." it's closer to seventy miles. They probably wanted to get to the city quicker. (00:17:20)
Suggested correction: It's 38 miles to drive down the M11 from Stansted to St Paul's cathedral - and about 20 as the crow flies.