Go to the smaller bars in London and always take a book - I find that people are a curious breed and someone will ask you what you are reading.
Small pubs -
The Rake in Covent Garden.
The French House - Soho.
The Campari Bar @The Polpo - Soho.
Also visit the Galleries:
The National Gallery - Trafalgar Square.
The Tate - Pimlico.
The Tate Modern - City.
At galleries many people tend to go on their own and many galleries have bars, so go in order a drink and who knows who you could meet.
It is also an idea to go to a cinema as many people go their alone too, many these days have bars so it would be the great place to hang out and perhaps discuss the movie you have just seen with someone else who happens to be alone.
I know all the above is alcohol based but at bars/cinemas/galleries as you know tea and coffee is also served.
Edited by Morgana142, 13 September 2012 - 07:15 AM.