So metal detection to search for historical artifacts is legal in UK, illegal in Ireland?
Firstly, the UK is three separate legal jurisdictions, each with their own rules on metal detecting: England/Wales, Scotland, Northern Ireland.
Secondly, these rules are not binary legal/illegal, but on a continuum of permissiveness. You always need some kind of permission. England/Wales is more permissive (where most non-protected land can be detected on with the landowner's permission) than the Republic of Ireland (where you need state approval to use a metal detector anywhere).
Some of the details here: https://detecthistory.com/metal-detecting/uk/
"It illegal to use a detection device to search for archaeological objects anywhere within the State or its territorial seas; without the prior written consent of the Minister for Culture, Heritage and the Gaeltacht"
(Note "anywhere")
https://www.museum.ie/en-ie/collections-research/the-law-on-...
Some good Samaritans sometimes send in Ireland's priceless heritage to the national museum. But of course they're not going to reveal who they are, or where they found it. They don't want to go to prison. So I guess we'll never know.
There are prohibitions and licensing requirements in both countries for search of heritage sites, national monuments, and other protected sites, and reporting requirements for unintentional "heritage" finds.