It's worth saying that both major parties are way out of line with the electorate on this - polling of whom shows:
there were consistent majorities for Remain from about mid-2017 until Brexit happened; and
there has been a consistent polling plurality for Rejoin pretty much since that point onwards (and sometimes outright polling majorities for Rejoin).
So neither of those parties are currently speaking for a large (and possibly majority) share of the electorate on this issue. When such situations arise, it's rare for the electorate to be the ones who have to change their mind and accord with what the politicians think...
What I expect will happen in the coming years (particularly after Labour go into government next year) is that the Lib Dems will get increasingly bolshy on this issue and probably build towards announcing a Rejoin manifesto in the run up to the 2028/9 general election, and Labour will start bleeding votes to them. That will force Labour to shift its position (in the same way they shifted their position on a People's Vote after the Lib Dems trounced them in Labour strongholds at the 2019 EU elections).
By the end of this decade, Rejoin will be a very mainstream position among British politicians in the way it already is with British voters.