As long ago as 1947 Lord Greene MR issued the seminal words on the topic in the famous case of AP Picture Houses v Wednesbury: The court will not substitute its own judgment of reasonableness over that of the person charged with the obligation to act reasonably. The bar for overturning a decision is much higher: “It must be proved to be unreasonable in the sense that the court considers it to be a decision that no reasonable body could have come to.”
It also illustrates that even the Master of the Rolls can end a sentence with a preposition.
In the commercial context, one often encounters the formulation “acting in a commercially reasonable manner”. There’s a good article there, if you’re interested.