my office used to be almost opposite the Chancery Court (lovely building, used to be the Pearl Assurance office - the hotel, not my office!).

going East towards the City from the hotel, you have the Farringdon/Smithfield area where recommendations would be:

Bleeding Heart - French
Smiths of Smithfield - British (specialising in meat)
Cafe du Marche - French
Dans le Noir - French but with the twist that you eat in the pitch dark

going south/west towards Aldwych/Strand/Covent Garden, recommendations would be:

Bank - Large and lively modern British
Simpson's in the Strand - very traditional English
Rules - very traditional English
the Savoy Grill - British (modern)
J Sheekey - traditional English fish restaurant
Neal Street Restaurant - Carluccio's flagship Italian (mushrooms with everything)

You should be able to find details of all of them on Square Meal