Depends a bit on which end of Fleet Street you are; at the Strand end the pubs/bars tend to be full of lawyers and at the other the clientele is more mixed.
If you walk down to the Embankment there's a Walkabout pub which is popular with a 'younger' crowd.
If you go into the City itself, the All Bar Ones have a bit of a reputation as 'pulling' places - M-F, M-M, F-F all included.
Go through into Smithfield and there are several trendy clubs/bars: Fabric (nightclub); Fluid (bar/club); Meet (bar/club); Smiths of Smithfield (bar on ground floor with good food; proper restaurants upstairs); and lots of pubs.
Depending on budget, of course, some of the CIty restaurants have good/fun bars: Coq D'Argent (over Bank tube station on Poultry); 1 Lombard Street; the Great Eastern Hotel; and the Pacific Oriental spring to mind.
Suggest you look at www.squaremeal.co.uk for the restaurants but it does also include bars; www.londonlater.com has information on late opening bars/restaurants/escort services etc.
Hope this helps.