The City of London is the name of an area of London, where the stock markets are etc. London is a city, but the actual "City of London" is an area between East and Central London. The City of London...
London has the Menelium, London Bridge, the London eye, Harrods, Hamleys, cities, Buckingham palace, Restaurant's, shops, Towers, Railway stations and Celebrities shopping and finally but not least...
If you are walking then it is 0.7 miles, because you would go over Victoria Embankment. However, if you are travelling by car or taxi then it is 1.5 miles, for you must cross the Waterloo Bridge.