What is the test for recovery of monies paid under mistake of fact?

The recovery of monies paid under mistake of fact is dependent upon the principle stated in Kelly v. Solari (1841), 9 M. & W. 54, 152 E.R. 24 [p. 26]: I think that where money is paid to another under the influence of a mistake, that is, upon the supposition that a specific fact is true, which would entitle the other to the money, but which fact is untrue, and the money would not have been paid if it had been known to the payer that the fact was untrue, an action will lie to recover it back, and it is against conscience to retain it; though a demand may be necessary in those cases in which the party receiving may have been ignorant of the mistake.