what trains are quick into charing cross?

Answer 1

You don't ask from where nor do you say what you mean by 'quick' so your question is rather difficult to answer with any accuracy. However, I can say Charing Cross has fast services to Hastings and the Kent Coast but none are as fast as, for example, the electric services to the north from King's Cross and Euston.

Answer 2

There are no trains which are quick into Charing Cross. There is a speed limit over Hungerford bridge of 25 mph between Waterloo East station (where every train stops) and the terminus.