In order to create a valid contract, the parties must have intended to create a legal relationship between them. This is usually obvious and in most commercial cases the court will presume that there was this intention. This criteria is only really seen in cases involving domestic or social contexts where the court presumes that there was no intention to create legal relations unless proved otherwise. The reasoning behind this is that as a matter of policy the court wants to avoid intruding too much into the private lives of families.
Where parties make an agreement in a domestic context the presumption is that they didn't intend to be legally bound. In Balfour v Balfour  2 KB 571, the parties were husband and wife. The husband went abroad and the wife claimed that he had promised to pay her ?30 per month. Atkin LJ explained the presumption by giving the example of an offer of hospitality and saying that ordinary, everyday agreements like that should not be governed by the law. Both parties would be able to sue each other for non-performance. He went on to say that it is normal for a husband and wife to make arrangements between themselves as to money and the presumption of no legal relations had not been rebutted.
A case where the presumption was rebutted is Merritt v Merritt  1 WLR 1211, where the Court of Appeal held that an agreement between husband and wife who had separated, was enforceable. The court distinguished Balfour on the basis that when spouses break up they want a clean split and so when they make agreements as to division of assets they intend for these to be enforceable. So ask what the state of the relationship was at the time the agreement was made.
In order to rebut the presumption, the parties cannot give evidence of their subjective thoughts. As with all contract law, the question of intention is judged objectively. The court will ask whether, objectively speaking, it appears that the parties had an intention for the agreement to be legally binding. This may be the case, as in Merritt, where the state of the relationship is deteriorating or has broken down. It is also possible to rebut the presumption by giving evidence that one of the parties acted to their detriment in reliance on the agreement. In Parker v Clark  1 WLR 286, the claimants agreed to give up their home and move in with an elderly couple. The couples had agreed to share expenses as long as the elderly couple left the house in their will to the claimants. The relationship broke down and the claimants left the house and started proceedings. The court held that there had been an intention to create legal arrangements and relied partly on how much the claimants had given up (they sold their house) in reliance on the agreement. The case may have been decided differently if the house had not been sold.
A presumption against intention to create legal relations exists in social contexts also. Relationship and reliance are also relevant factors for the purpose of rebutting a presumption. In Simpkins v Pays  1 WLR 975, the Claimant lived with D as a lodger. Each week the C , D and D's granddaughter enter a newspaper competition. C filled out the coupon in the defendant's name. They shared the postage fee. One week they won ?750 and D refused to pay C a one third share. She alleged the agreement was not intended to be legal. The court held that even though the agreement was informal it was intended to be legal.
The presumption that the parties intended to create legal relations in a commercial context is rarely rebutted. The parties can rebut it by expressly agreeing that they do not want legal relations to arise. However, if the Defendant is trying to rebut the intention they may as well argue that no contract existed at all. They are essentially the same thing.