I think in 2016 there was a petition about holding a second referendum under certain conditions -- perhaps that's the one you meant got 800k signatures from the Vatican?
Back then I think it was much easier to sign petitions on that site. These days you need a postcode and an email address, and have to confirm that the email address is in use, so it is at least a little harder to game the system. Using postcodes probably also helps because it would be impossible, for example, for any constituency to report more signatories than there are constituents. Moreover that same data allows you to check which regions are most commonly signing the petition, and lo and behold, they match pretty well remain-supporting areas in 2016.
In short, this petition is at least *mostly* genuine. I will be interested to see if it ever gets up to referendum levels, but it hardly needs to in order to matter.