As others have said, all that they are asking for is the balance outstanding on the amount that you agreed to pay at the outset. So yes you do owe the money. From a legal point you might be able to claim estoppel (see last night's thread on that !) but i don't think the case will be strong.
You could offer to pay it in instalments over maybe 3 months and they may accept that, or you could ask for a discount for the inconvenience (tell them you have now spent the money and will need to take out a loan)