This isn't really all that difficult a moral decision.
Was the quote accepted on a fixed price basis or Time & Materials basis?
If the former then you took the risk and get the reward too. If it'd cost you more you would have lost profit without recourse to the customer. You may well have made £2K by accident but it's yours.
If T&M then the customer took the risk and should also get the benefit. Thus if it cost you less then you should, in all fairness, invoice a proportionally lesser amount.
If there is an error in your pricing then I'd inform the client and refund the money. Your reputation is worth more than £2k.