That would require Freedom Of Movement, which from my experience living in the UK at the time of the Leave Referendum was the main thing driving the Leave vote, closely followed by the UK having to follow EU directives (i.e. the whole “sovereignty” malarkey).
Looking around (not the just UK), xenophobia has become even stronger since, not weaker and Norway-style is still mainly “following EU directives”, though with some opt-outs in things not to do with Trade or Freedom Of Movement.
Also this time around it would be Spain as an EU member whilst the UK tried to get in (the reverse of last time) so they would probably demand to get Gibraltar back as condition for their vote (which is required since a unanimous vote is required). More in general pretty much any EU member with a bone to pick with the UK would get their chance, which might also be interesting for the likes of Greece (better make sure there isn’t a leftwing government in Greece given how the UK literally intervened militarilly to make sure at the end of WWII that the Fascists ended up in power in Greece, a dictatorship that lasted until the 80s).