An agreement is the consent of two or more persons to form some engagement, or to rescind or modify and engagement already made
Boulton v Jones (1857) 2 H & N 564; 27 U Ex 117, per Pollock CB at p.118-119:
Now the rule of law is clear, that if you propose to make a contract with A, then B cannot substitute himself for A without your consent and to your disadvantage, securing to himself all the benefit of the contract.
Bramwell B in his judgment stated at p.118:
I do not lay it down that because a contract was made in one person’s name another person cannot sue upon it, except in cases of agency. But when any one makes a contract in which the personality, so to speak, of the particular party contracted with is important, for any reason, whether because it is to write a book or paint a picture, or do any work of personal skill, or whether because there is a set-off due from that party, no one else is at liberty to step in and maintain that he is the party contracted with, that he has written the book or painted the picture, or supplied the goods; and that he is entitled to sue, although, had the party really contracted with sued, the defendant would have had the benefit of his personal skill, or of a set-off due from him.
In W J Rossiter v Miller (1870) 3 App Cas 1124 Lord Blackburn said at p1151:
So long as they are only in negotiation either party may retreat; and though the parties may have agreed on all the cardinal points of the intended contract, yet, if some particulars essential to the agreement still remain to be settled afterwards, there is no contract. The parties in such a case are still only in negotiation but the mere fact that the parties have expressly stipulated that there shall afterwards be a formal agreement prepared embodying the terms which shall be signed by the parties, does not, by itself show that they continue in negotiation.
Cundy v Lindsay (1878) 3 App Cas 459, per Lord Cairns LC at pp. 464-465:
how is it possible to imagine that in that state of things any contract could have arisen between the respondents [plaintiffs] and Blenkarn, the dishonest man? Of him they knew nothing, and of him they never thought. With him they never intended to deal. Their minds never, even for an instant of time, rested upon him, and as between him and them there was no consensus of mind which could lead to any agreement or any contract whatever.
and Lord Hatherley at p. 469 said:
from beginning to end the respondents believed they were dealing with Blenkiron & Co, they made out their invoices to Blenkiron & Co, they supposed they sold to Blenkiron & Co, they never sold in any way to Alfred Blenkarn; and therefore Alfred Blenkarn cannot, by so obtaining the goods, have by possibility made a good title to a purchaser, as against the owners of the goods, who had never in any shape or way parted with the property nor with anything more than the possession of it.
Statement by Lord Phillips of Worth Matravers in Shogun Finance Ltd v Hudson  1 AC 919 at p.964:
 A contract is normally concluded when an offer made by one party ("the offeror") is accepted by the party to whom the offer has been made ("the offeree"). Normally the contract is only concluded when the acceptance is communicated by the offeree to the offeror. A contract will not be concluded unless the parties are agreed as to its material terms. There must be "consensus ad idem". Whether the parties have reached agreement on the terms is not determined by evidence of the subjective intention of each party. It is, in large measure, determined by making an objective appraisal of the exchanges between the parties. If an offeree understands an offer in accordance with its natural meaning and accepts it, the offeror cannot be heard to say that he intended the words of his offer to have a different meaning. The contract stands according to the natural meaning of the words used. There is one important exception to this principle. If the offeree knows that the offeror does not intend the terms of the offer to be those that the natural meaning of the words would suggest, he cannot, by purporting to accept the offer, bind the offeror to a contract: Hartog v Colin & Shields  3 All ER 566; Smith v Hughes (1871) LR 6 QB 597. Thus the task of ascertaining whether the parties have reached agreement as to the terms of a contract can involve quite a complex amalgam of the objective and the subjective and involve the application of a principle that bears close comparison with the doctrine of estoppel. Normally, however, the task involves no more than an objective analysis of the words used by the parties. The object of the exercise is to determine what each party intended, or must be deemed to have intended
 Just as the parties must be shown to have agreed on the terms of the contract, so they must also be shown to have agreed the one with the other. If A makes an offer to B, but C purports to accept it, there will be no contract. Equally, if A makes an offer to B and B addresses his acceptance to C there will be no contract. Where there is an issue as to whether two persons have reached an agreement, the one with the other, the courts have tended to adopt the same approach to resolving that issue as they adopt when considering whether there has been agreement as to the terms of the contract. The court asks the question whether each intended, or must be deemed to have intended, to contract with the other. That approach gives rise to a problem where one person is mistaken as to the identity of the person with whom he is dealing, as the cases demonstrate.
Per Lord Justice Toulson in Papas Olio JSC v Grains & Fourrages SA & Anor  EWCA Civ 1401 at para 28:
28. It is commonplace in commercial life, particularly in markets where the use of standard forms of contract is common, for parties to agree on all the essential terms necessary to bring about the conclusion of an oral contract and for the oral contract then to be followed by a written document, often described as a confirmation or recap, which will not only set out the essential terms but other terms common in the market. If there is no comeback from the other party, it may be easy to infer assent. The situation would be very different if there was no prior oral contract. Where the oral contract is followed by a written confirmation setting out fuller terms to which the other party is judged by the fact finder to have assented, it is of no practical importance whether the situation is analysed as the parties as having entered into a partly oral and partly written contract or as having entered into a written contract. Probably the better analysis is that the written document fulfils a dual function; it both confirms evidentially the making of the oral agreement but also supersedes the oral agreement in that it provides a document to which the parties thereafter look as the expression of their bargain.