I am a lawyer. This is English law, so does not apply elsewhere. It is not advice and should not be relied on without consultation with a solicitor on your own circumstances.
At law, there is usually nothing wrong with bidding on your own auction provided that you make it clear in the auction conditions that your right to bid on your own item is reserved. The right is specifically reserved in land transactions by the Sale of Land by Auction Act 1867, but is of general application.
In this case though, there cannot be a reservation because it is against the auctioneer's rules to bid on your own item. In that case, as mentioned above, the Fraud Act comes into play. For what it's worth it would have been unlawful at common law prior to the Fraud Act coming into force, but that's not relevant to this situation. Section 1(1) provides that "A person is guilty of fraud if he is in breach of any of the sections listed in subsection (2)." Section 2(1) states "A person is in breach of this section if he—
(a)dishonestly makes a false representation, and
(b)intends, by making the representation—
(i)to make a gain for himself or another, or
(ii)to cause loss to another or to expose another to a risk of loss."
A bid is a representation to the auctioneer and to other bidders, and therefore the bid is a fraud under the Act. There are other ways that this behaviour could be fraudulent too.
As for making offers on property in writing and getting written acceptance, that can amount to a contract, but I would not advise any buyer to do this. At the time of the offer, there will usually have been no investigation of title, or searches to ensure that the property is one you relly want to buy. So you might find that you are contractually bound to buy a property with subsidence, next to a planned 6 lane motorway and the seller doesn't have absolute title to the land.