The YMCA here has a second-hand furniture shop, and a recycled electrics shop, Kathy, so I bet there's one somewhere in your county. They take virtually anything, and have a proper removals truck with men to handle the stuff.
Alternatively, there are many charities which struggle to find the funding for office furniture (people like to give towards funding medicine, aid, etc., not office desks!), so a trawl under the 'Charities' heading in your Yellow Pages might find some very grateful people. Any which give advice will work from office environments - Victim Support, Headway, the NSPCC, Age Concern, Help the Aged, or perhaps even your local hospice might need some office stuff? Round here, the Martlets Hospice is funded by charity, and run from offices, as are Macmillan Nurses.
Additionally, your local British Legion, Rotary, or Lions Clubs should have a good idea of the state of the charities they support - chances are they'll know who could benefit from your kind gesture. And many charities supporting addicts and the homeless could sometimes use the odd bit of furniture for their admin work.
Jft: auction houses struggle to sell any furniture nowadays. Kathy would be lucky to see £10 a desk, and then have to pay 16.5% commission out of whatever she got. The YMCA here sells donated wardrobes at around £30, and office desks would probably be saleable for £10-30 each depending on condition. On the other hand, many charities can't find people willing to donate towards materiel - only towards what they actually do!