Where … certain legal consequences are only attached to the act if it is accompanied by a particular intention, proof of a mistake may show that such intention did not exist in the case in question.
Smith v Hughes  6 QB 597, per Blackburn J:
In this case I agree that on the sale of a specific article, unless there be a warranty making it part of the bargain that it possesses some particular quality, the purchaser must take the article he has bought though it does not possess that quality. And I agree that even if the vendor was aware that the purchaser thought that the article possessed that quality, and would not have entered into the contract unless he had so thought, still the purchaser is bound, unless the vendor was guilty of some fraud or deceit upon him, and that a mere abstinence from disabusing the purchaser of that impression is not fraud or deceit; for, whatever may be the case in a court of morals, there is no legal obligation on the vendor to inform the purchaser that he is under a mistake, not induced by the act of the vendor.’
Tamplin v James [1874-80] All ER Rep. 562, CA, per James LJ:
The defence on the ground of mistake cannot be sustained. It is not enough for a purchaser to swear, 'I thought the farm sold contained twelve fields which I knew, and I find it does not include them all', or, 'I thought it contained 100 acres and it only contains eighty'. It would open the door to fraud if such a defence was to be allowed. Perhaps some of the cases on this subject go too far, but for the most part the cases where a Defendant has escaped on the ground of a mistake not contributed to by the Plaintiff, have been cases where a hardship amounting to injustice would have been inflicted upon him by holding him to his bargain, and it was unreasonable to hold him to it. It is said that it is hard to hold a man to a bargain entered into under a mistake, but we must consider the hardship on the other side. … If a man makes a mistake of this kind without any reasonable excuse he ought to be held to his bargain.
Lord Atkin in Bell v Lever Bros Ltd  AC 161,  All ER Rep 1, stated:
'… the rules of law dealing with the effect of mistake on contract appear to be established with reasonable clearness. If mistake operates at all it operates so as to negative or in some cases to nullify consent. The parties may be mistaken in the identity of the contracting parties, or in the existence of the subject-matter of the contract at the date of the contract, or in the quality of the subject-matter of the contract. These mistakes may be by one party, or by both, and the legal effect may depend upon the class of mistake above mentioned. Thus a mistaken belief by A. that he is contracting with B., whereas in fact he is contracting with C., will negative consent where it is clear that the intention of A. was to contract only with B. So the agreement of A. and B. to purchase a specific article is void if in fact the article had perished before the date of sale.
…I have come to the conclusion that it would be wrong to decide that an agreement to terminate a definite specified contract is void if it turns out that the agreement had already been broken and could have been terminated otherwise. The contract released is the identical contract in both cases, and the party paying for release gets exactly what he bargains for. It seems immaterial that he could have got the same result in another way, or that if he had known the true facts he would not have entered into the bargain. A. buys B.’s horse; he thinks the horse is sound and he pays the price of a sound horse; he would certainly not have bought the horse if he had known as the fact is that the horse is unsound. If B. has made no representation as to soundness and has not contracted that the horse is sound, A. is bound and cannot recover back the price. A. buys a picture from B.; both A. and B. believe it to be the work of an old master, and a high price is paid. It turns out to be a modern copy. A. has no remedy in the absence of representation or warranty. A. agrees to take on lease or to buy from B. an unfurnished dwelling-house. The house is in fact uninhabitable. A. would never have entered into the bargain if he had known the fact. A. has no remedy, and the position is the same whether B. knew the facts or not, so long as he made no representation or gave no warranty. A. buys a roadside garage business from B. abutting on a public thoroughfare: unknown to A., but known to B., it has already been decided to construct a byepass road which will divert substantially the whole of the traffic from passing A.’s garage. Again A. has no remedy. All these cases involve hardship on A. and benefit B., as most people would say, unjustly. They can be supported on the ground that it is of paramount importance that contracts should be observed, and that if parties honestly comply with the essentials of the formation of contracts - i.e., agree in the same terms on the same subject-matter - they are bound, and must rely on the stipulations of the contract for protection from the effect of facts unknown to them.
In Associated Japanese Bank (International) Ltd v Crйdit du Nord SA  3 All ER 902 at 912,  1 WLR 255 at 268 Steyn J stated on the rules concerning mistake that:
Logically, before one can turn to the rules as to mistake, whether at common law or in equity, one must first determine whether the contract itself, by express or implied condition precedent or otherwise, provides who bears the risk of the relevant mistake. It is at this hurdle that many pleas of mistake will either fail or prove to have been unnecessary. Only if the contract is silent on the point is there scope for invoking mistake.
Great Peace Shipping Ltd v. Tsavliris Salvage (International) Ltd  EWCA Civ 1407,  2 All ER (Comm) 999 per Lord Phillips of Worth Matravers MR at p.1006 :
 A mistake can be simply defined as an erroneous belief. Mistakes have relevance in the law of contract in a number of different circumstances. They may prevent the mutuality of agreement that is necessary for the formation of a contract. In order for two parties to conclude a contract binding in law each must agree with the other the terms of the contract. Whether two parties have entered into a contract in this way must be judged objectively, having regard to all the material facts. It may be that each party mistakenly believes that he has entered into such a contract in circumstances where an objective appraisal of the facts reveals that no agreement has been reached as to the terms of the contract…
 … More commonly an objective appraisal of the negotiations between the parties may disclose that they were at cross-purposes, so that no agreement was ever reached. In such a case there will be a mutual mistake in that each party will erroneously believe that the other had agreed to his terms…
 Another type of mistake is that where the parties erroneously spell out their contract in terms which do not give effect to an antecedent agreement that they have reached. Such a mistake can result in rectification of the contract…
 … what we are here concerned with is an allegation of a common mistaken assumption of fact which renders the service that will be provided if the contract is performed in accordance with its terms something different from the performance that the parties contemplated. This is the type of mistake which fell to be considered in Bell v Lever Bros Ltd  AC 161,  All ER Rep 1. We shall describe it as 'common mistake', although it is often alternatively described as 'mutual mistake.
Lord Justice Sedley said in George Wimpey UK Ltd v VI Construction Ltd  EWCA Civ 77:
 The phrase 'honest and reasonable' is not a term of art. It is a judicial attempt to sketch a line beyond which conduct may be regarded as unconscionable or inequitable. Its duality, however, is a recognition that honesty alone is too pure a standard for business dealings because it omits legitimate self-interest; while reasonableness alone is capable of legitimising Machiavellian tactics.
 Mistake is a concept which sits awkwardly in this space. Absent a prior accord which has simply not been carried into effect, absent also a dishonest inducement to contract, one is looking for a mistake on the claimant’s own part which the defendant was honour-bound, despite his own legitimate business interests, to point out to him. I am unable to accept that this was such a case on any tenable view of the evidence.
 There are at least two kinds of mistake. One is a literal misunderstanding of some fact material to the proposed contract. The other is an error of judgment in entering into the contract. I find it difficult to think that the second kind has any relevance to the law of unilateral mistake. Nobody is bound, even in honour, to help his opposite number to negotiate to the best advantage.