But speaking to ITV News, the Secretary of State for Culture, Media and Sport Lisa Nandy said she said: "I'm slightly baffled as to why anybody would think that the only answer to the absolute kicking that Labour got at the polls last Thursday is Europe."
I don't think that it's likely realistic from a policy standpoint, but my understanding from past reading is that a major reason for post-Brexit Con/Lab party support fragmentation is that Brexit became a new political issue and people restructured identities around it. Because Leave/Remain didn't align all that well with existing party lines, it caused disintegration as new fissures emerged, so making "Leave" or "Remain" a partisan issue might eliminate that fragmentation.
My understanding from a policy standpoint is that, among other issues, a major problem for a near-term Rejoin is that there's only majority British support for Rejoin if the UK gets its opt-outs back, and that it's expected that it would be quite unlikely for the EU to make an offer containing those opt-outs (like, EU members that got told "no, you can't have any opt-outs yourself, because we're done with offering those" would need to go and unanimously grant them to the UK after not being permitted them themselves, which would be quite difficult to sell politically in those countries).