HMS Victory, which was launched in 1737 and built in Portsmouth, was lost in a storm off the Channel Islands in 1744, while under the command of Admiral Sir John Balchin.
The wreck was found in the English Channel near Torbay, Devon, in 2008. Defence ministers have decided that artefacts should stay on the wreck and be preserved in situ.
The Maritime Heritage Foundation, a charity chaired by Lord Lingfield - a descendant of Sir John Balchin - wanted to remove artefacts for preservation and challenged that Ministry of Defence decision.
But a judge has dismissed the foundation's challenge after analysing evidence at a High Court hearing in London.
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Mrs Justice Lieven said on Friday, in a written ruling, that the ministry's decision was lawful and not irrational.
She said HMS Victory was a British Navy flagship and the wreck contained at least 41 bronze cannons, ship-borne artefacts, iron ballast, wooden fixtures and fittings, parts of two anchors and a rudder.
The judge said there had been claims the ship may have been carrying gold bullion.
But she said there was no ‘direct evidence’ to support such claims.
Mrs Justice Lieven said the Ministry of Defence had concluded that the wreck was at ‘minimal risk’ and could be "appropriately monitored".
She said officials had ‘fully engaged’ with the foundation throughout the decision-making process.
Five years ago then defence secretary Sir Michael Fallon had said the foundation could recover some ‘at-risk’ artefacts, but had subsequently changed his mind.
An HMS Victory website, www.victory1744.org , developed by the Maritime Heritage Foundation, tells how the ship was the predecessor of Nelson's Victory.
The website says the man of war, which was built in Portsmouth, Hampshire, was the ‘greatest warship in the age of sail’ and Sir John Balchin one of the most respected and longest-serving fighting officers in Royal Navy history.
It says the ship disappeared with all hands on October 5 1744.
‘One of the most impressive features was her full complement of ordnance, one of the largest consignments of bronze guns ever manufactured,’ says the website.
‘Historically, the Victory marks the final flourish in the life of bronze cannon on English warships ... the Royal Navy phased out their production in favour of cheaper iron guns.’