He granted an injunction sought by Harrogate Borough Council ordering the couple to demolish the barn, which they claim cost them £100,000 to build, and will cost a further £40,000 to tear down.
Setting out what he found was the Crosslands’ "reprehensible" conduct, the judge said: "After four previous rejections of what was, to all intents and purposes, the same barn, the defendants again gave notice of their intention to carry out what they claimed was permitted agricultural development.
"The notice was accompanied by £45, when the correct fee was £50. Despite that, the council notified the defendants that prior approval for the development was required, in accordance with the statutory provisions.
"A few days later, the defendants sent the missing £5 under cover of a letter that was in almost exactly identical terms to their first notice. The council did not repeat what they had said a few days earlier, that prior approval was required.
"The defendants now maintain that it was only the sending of the additional £5 which validated their original application, so that the council’s earlier notification was in respect of an invalid application, and was therefore itself invalid.
"In the absence of any further notification from the council, the defendants say that, under the relevant statutory provisions, planning permission was given by default."
The judge said that the field is located within the Nidderdale Area of Outstanding Natural Beauty, which is "amongst the most beautiful parts of a county richly endowed with such wild uplands".
He said that the Crosslands keep ewes on the land and have been seeking to build a barn there since they bought it in 2003.
However, the council has repeatedly rejected their claims that the barn would constitute permitted agricultural development, on the basis that it would have a harmful impact on the open nature of the land.
The judge said that they have made similar unsuccessful applications in relation to other land they own on nearby Menwith Hill Road, and had attempted a similar plan to manipulate the planning process in respect of that site.
Despite the council’s stance, construction works began at the Meagill Lane field in late 2010 or early 2011, and only came to and end in June or July 2012, by which time it had three complete walls and the steel roof structure in place, together with some internal blockwork.
Rejecting the couple’s case, the judge said that they had sought to "play the system" and that they took a "clear and calculated risk in going ahead with the construction of the barn" when an enforcement notice issued in 2006 remained in force.
He said: "I can only conclude that the underpayment was deliberate. Whilst it is unclear precisely what advantage they thought they might achieve by paying less than the full fee, I am in no doubt that it was the first step in a process by which the defendants sought to manipulate the planning process for their own benefit."
He continued: "I am bound to say that I consider that the conclusion that the council acted properly and fairly, whilst the defendants’ case was a mix of the technical and the sly, and should fail, is a result which would generally commend itself as a practical and sensible outcome.
"Anything else would result in an injustice and would come uncomfortably close to allowing the defendants to take advantage of their own wrong."
Ruling that an injunction should be granted requiring demolition of the barn, he continued: "I conclude that this partially-built barn was not reasonably necessary for the purposes of agriculture within the defendant’s farm. It was not designed for the purposes of the activities which the defendants might reasonably conduct on their farm."
"I have concluded that there was no valid planning permission for this barn. In those circumstances, I consider that there is an overwhelming case for the court to exercise its discretion in favour of an injunction, requiring the demolition of the partially-built barn."
The judge also cast doubt on the figures put forward by the couple as to the expense of constructing and demolishing the barn, and said: "Of course, it is a great shame that, when the injunction is granted, any money that the defendants have spent on the barn will be wasted. But the defendants knew or must have known that they were spending such money at their own risk.
"This was a deliberate decision to build as much of the barn as possible so that they could better run the argument that it would be a waste if it was demolished. That is another way of effectively playing the system. I cannot refuse the injunction because it would involve the defendants in wasted expenditure in circumstances where the defendant has caused that waste themselves."