I've been to many auctions and I've met many antique dealers. I know that they rarely, if ever pay, more than a third of the price that they'll later sell an item for but they usually start by offering only around 10% of their saleroom price. So my way of looking at your situation is this:
Let's say that you've got an item of furniture that will sell for £500 in an antique dealer's shop. If you invite him around to your home, he'll probably offer you £50 for it but, if you push him a bit, he might go up to perhaps £80.
If you put the same item up for sale at auction though, the same dealer will, once again, start off with a £50 bid. However other dealers will then push the bidding up to £150 (because that's close to the one third cut-off point that they tend to work to). You might perhaps pay 15% commission + VAT = 18% in total, which comes to £27. That will still leave you with £123, which is a lot more than you'd have got if Dealer Number 1 hadn't faced any competition in the bidding.
So I'd recommend going down the auction route. (If you're lucky, there might be a private buyer at the auction, who would like your furniture for their own home. If so, they might be prepared to bid a bit more than any of the dealers will. If you're really lucky, there might be two private buyers at the auction, competing against each other, who end up bidding more than the showroom price!)