I don't think they're claiming copyright; that's just a boilerplate statement alluding to the fact that just because you see it here on the public internet doesn't mean you shouldn't do your own research to find out whom if anyone has copyright.

You can claim whatever you want. You can claim the sky is made of cheese. Don't make it true.

It's debatable whether, under UK law, you can claim copyright on an image that's just a straight scan of a public-domain/out-of-copyright image. Usually you need to do some sort of work to get the "sweat of the brow" copyright protection. Though it's quite common for places that scan images (like libraries) to claim copyright.

This is a big problem when OpenStreetMap mappers want to trace from an old map.

British copyright law is relatively strict. Given that these were submissions to a royal competition it's entirely possible they're subject to perpetual crown copyright.

I believe in the UK you can hold the copyright to the scan/photo of an artwork or image that is out of copyright. So the digital versions of these images are relatively new and the copywrite would be held by the person making the copy.

You can, but see https://www.gov.uk/government/uploads/system/uploads/attachm...

Are digitised copies of older images protected by copyright?

Simply creating a copy of an image won’t result in a new copyright in the new item. However, there is a degree of uncertainty regarding whether copyright can exist in digitised copies of older images for which copyright has expired. Some people argue that a new copyright may arise in such copies if specialist skills have been used to optimise detail, and/or the original image has been touched up to remove blemishes, stains or creases.

However, according to the Court of Justice of the European Union which has effect in UK law, copyright can only subsist in subject matter that is original in the sense that it is the author’s own ‘intellectual creation’. Given this criteria, it seems unlikely that what is merely a retouched, digitised image of an older work can be considered as ‘original’.

That is an interesting concept. So is it possible to create multiple copyrighted versions of an artwork or image that is out of copyright?

It's possible to create multiple derivative works of an out-of-copyright work, each of which will carry its own copyright. E.g. modern Sherlock Holmes stories. The question that matters is whether the scan involved enough creative work to qualify for copyright in its own right; as the sibling says, a simple scan won't, but a thorough restoration might.