Even if you bought this new from a high street store you would have no right to a refund under the current laws.
The laws for second hand goods are the same:
"When you make a purchase from a second-hand shop, you can exercise exactly the same rights under the Sales of Goods Act as you can with a high-street shop that sells new items. This means that if the item is not fit for purpose or is faulty, you can demand a refund.
But if you merely change your mind about a purchase, a second-hand shop – just like any other – is under no legal obligation to provide a refund or even a return. “Instead, each shop will operate its own returns policy, which you agree to when you make the purchase,” says a spokesperson from the Citizens Advice Bureau."
http://www.moneywise.co.uk/cut-your-costs/shop-smart/your-rights-when-buying-second-hand-goods
In your case if the piece of furniture had been wrongly described such as '3 foot chest' when it is 3 foot 3 you would be entitled to a full refund. If there was no such description, you aren't.
However, the item had not left the shop before you cancelled it and I do think the shop has been harsh.