Per Hannen J. in Smith v Hughes  6 QB 597
It is essential to the creation of a contract that both parties should agree to the same thing in the same sense. Thus, if two persons enter into an apparent contract concerning a particular person or ship, and it turns out that each of them, misled by a similarity of name, had a different person or ship in his mind, no contract would exist between them: Raffles v Wichelhaus (1864) 2 H & C 906.
R v Davies  1 All ER 513, per Eveleigh LJ at p.515:
If the ladies did not know they were indorsing a cheque on the piece of paper that was there before them to write on, and if Mr Davies thereafter obtained those pieces of paper from them, that is to say the cheques, although unknown to be such by the ladies, the property, in the form of the cheques, did not pass. Indeed, it is quite the contrary because the mind of the alleged donor would not have gone with the transaction, of handing over the cheques, intentionally parting with possession of those very cheques, doing so in a way so as to transfer the ownership of them. The mind of the donor simply would not have gone with the gift at all. It follows, as night follows day, that if they did not know they were signing the cheques, but gave the accused the pieces of paper, they were clearly not intending to give a cheque. Consequently, the property, in other words those cheques, never passed to the accused at any time.
Per Lord Diplock in Paal Wilson & Co A/S v Partenreederei Hannah Blumenthal(The Hannah Blumenthal),  1 All ER 34 at pp.48-49:
To create a contract by exchange of promises between two parties where the promise of each party constitutes the consideration for the promise of the other what is necessary is that the intention of each as it has been communicated to and understood by the other (even though that which has been communicated does not represent the actual state of mind of the communicator) should coincide. That is what English lawyers mean when they resort to the latin phrase 'consensus ad idem' and the words that I have italicised are essential to the concept of 'consensus ad idem', the lack of which prevents the formation of a binding contract in English law.
Thus if A (the offeror) makes a communication to B (the offeree), whether in writing, orally or by conduct, which, in the circumstances at the time the communication was received, (1) B, if he were a reasonable man, would understand as stating A’s intention to act or refrain from acting in some specified manner if B will promise on his part to act or refrain from acting in some manner also specified in the offer, and (2) B does in fact understand A’s communication to mean this, and in his turn makes to A a communication conveying his willingness so to act or to refrain from acting which mutatis mutandis satisfies the same two conditions as respects A, the 'consensus ad idem' essential to the formation of a contract in English law is complete.