What is the test for an arbitrator to enforce a contract where the contract is not enforceable?

The arbitrator later sets out the principle as enunciated by Denning L.J. in Combe v. Combe, [1951] 1 All E.R. 767 at p. 770. That exposition of the doctrine was as follows: The principle, as I understand it, is that where one party has, by his words or conduct, made to the other a promise or assurance which was intended to affect the legal relations between them and to be acted on accordingly, then, once the other party has taken him at his word and acted on it, the one who gave the promise or assurance cannot afterwards be allowed to revert to the previous legal relations as if no such promise or assurance had been made by him, but he must accept their legal relations subject to the qualification which he himself has so introduced, even though it is not supported in point of law by any consideration, but only by his word. Elsewhere, Denning L.J. is said to have explained that the doctrine is only applicable where the parties have already entered into a definite and legal contractual or analogous relationship, when there exists some conduct or promise which induces the other party to believe that the strict legal rights under the contract will not be enforced or will be kept in suspense and that "having regard to the dealings which have taken place between the parties" it will be inequitable to allow that party to enforce their strict legal rights.