In the UK, if a property doesn't sell at auction the property will be moved into a ‘post-auction sale' in which interested parties will be invited to make their highest offer on the property and the seller will decide if they wish to still sell.
If so, any post-auction sale will be agreed under auction conditions, with the same rules, agreements and fees applied as if the house sold during the original auction.
Therefore, if a house fails to sell at auction initially, it doesn't mean that it's time for the seller, nor potential buyer, to give up hope.