The 18th century urns were located at Marcus Dill's home, Idlicote House near Shipston-on-Stour, before he sold them at auction in 2009.
It was not until 2014 that Stratford-on-Avon District Council became aware that the urns and pedestals had been removed and began correspondence with Dill.
Dill made a retrospective application for listed building consent to remove them, but the council refused the application and issued the enforcement notice in April 2016.
Dill explained that the items had been shipped abroad after he sold them for £55,000. He doesn't even know the purchaser's name and he has no way of getting them back, his barrister Richard Harwood QC told the Appeal Court.
Council planners argued that to grant retrospective consent for the urns' removal would set "an extremely dangerous precedent".
Dill had argued that the urns and pedestals are not "buildings" and should never have been listed. But the council said the removal of the urns and pedestals "equated to demolition" and that "substantial harm had been caused".
The enforcement notice was later confirmed by a planning inspector, who pointed out that all sorts of structures - from telephone and post oxes to shipyard cranes, as well as "sculpture or statuary" - are on the listed buildings register. The inspector's decision was backed by the High Court last year.
Yesterday that order was upheld by the Court of Appeal , meaning Dill could face a criminal trial if he fails to comply. Lord Justice Hickinbottom rejected his arguments that the urns and pedestals are not "buildings" and should never have been listed.
The judge said it was Parliament's intention that the appearance of even moveable items on the listed buildings register should be decisive.
Lords Justice McCombe and Coulson agreed with him that the status of the urns and pedestals as listed buildings was beyond question and "could not be challenged".
Dismissing Dill's appeal, the court also ruled his retrospective application for listed building consent invalid because it did not state to where the urns and pedestals had been moved.
Dill was already facing substantial legal costs before his appeal, and the judges today added another £6,485 to his bill.
Yesterday, a High Court judge overturned a decision by former communities secretary Sajid Javid to refuse plans for an opencast mine in Northumberland on grounds including the scheme's potential impact on climate change.
Last week, a High Court judge dismissed a claim that a planning inspector overstepped her powers in approving a developer's application to revise conditions imposed on a planning permission and increase the height of two wind turbines in west Wales by 25 per cent.
And also last week, a Warwickshire farmer failed in a High Court bid to overturn a council's decision to discharge a planning condition stipulating that the developer of a neighbouring barn conversion must install acoustic fencing to prevent possible noise complaints from future residents of the property.