If you ask a Londoner where the center of London is, you are likely to get a wry smile. This is because, historically, London was two cities: a commercial city and a separate government capital.
However, the point from which distances to "London" are measured is in Trafalgar Square, where the original Charing Cross stood.
The commercial capital was the City of London. This had a dense population and all the other prerequisites of a medieval city: walls, a castle (The Tower of London), a cathedral (Saint Paul's), a semi-independent city government, a port and a bridge across which all trade was routed so Londoners could make money (London Bridge).