According the AA Route Planner (GB Edition) the distance is 6.1 miles, this will take about 0 hours and 20 minutes to drive or take a taxi, assuming you take the direct route to the centre of each...
The area of Charing Cross is on the site of the former hamlet of Charing which had a statue or cross called the Eleanor Cross - now long demolished.
4.47 kilometres (2.78 miles)
8.98 kilometres (5.58 miles)
13.91 kilometres (8.64 miles)