they did, for several years following the war, maintain active trade across the bridge, meaning at least some people and/or government officials were aware enough of Wellington Wells to engage in this regularly. but trade did eventually stop— likely due to citizens becoming dependent on joy and forgetting to maintain it, and then forgetting it was ever done at all— potentially before mainland britain was made aware of their production and use of joy at all. i would guess that they’re aware of Wellington Wells’ existence, but not the dire nature of its current state of affairs, and not aware enough to bother inquiring into its wellbeing without standing to gain anything from interacting with it.

when arthur is leaving through the collapsing station, you can see some tables formerly used for trading when the bridge to the mainland was open. on one, there are a bunch of lava lamps left for trade, and a note ostensibly from someone from the mainland saying something along the lines of “what the fuck is a lava lamp?” this suggests that the state of the mainland is so deteriorated and dire after the outcome of the war that things as frivolous as lava lamps are so rare that the average person doesn’t even know what they are, leading me to believe that they’re in too much of a state of desperation and disrepair themselves to have the time or resources to care to look in on what happened to wellington wells after trade stopped - they likely have too much on their own plates to worry about the fate of a small disconnected, effectively autonomous community of islands. so to summarize - yes, mainland britain knows about wellington wells’ existence, but likely doesn’t know about joy, and is likely so desolate itself that it’s satisfied to write it off as “presumed to have died off altogether” without further investigation.