It's perfectly lawful to run an auction in the way you suggest. Since you'll be selling your own property (or selling for others on a 'no profit' basis) you won't be running a business, so there's no need to tell the tax man about it. (If you charged a buyer's premium or commission on the sale of other people's goods you'd have to pay income tax on your profits). There is no other relevant legislation to worry about.
If you're a bit of a 'showman,' running an auction (and acting as auctioneer) can be great fun. I've done it for several charities and really enjoyed it. Just make sure that you clearly state when viewing can take place and whether bids can be left by those unable to be present when you put items under the hammer. Also make it clear how quickly purchasers must remove large items from the house. (You probably won't want to get a good sum for a large item of furniture only to be told that the buyer can't get hold of his mate's van, in order to shift it, until the week after next!).
Chris