There is one snag in that plan. EU doesnt want UK back, at lest not for another 5-10 years.
But, from my POV, UK is just too desirable and powerful.
(I don't belong to UK, by the way)
You have to consider that the EU is not monolithic. The UK that pushed to get southern and eastern countries into the union to grow the trade power of the customs union. France and some other EU countries probably would have preferred a more "core Europe" of countries of similar wealth and histories.
France gains in many ways if the UK stays out. It becomes the only member that can really project military power. France and the UK were often at odds about what the EU should be.
Until Germany wakes up from their dream, which it looks they did after the Ukrainian invasion and the 100 billion euro budget for the Bundeswehr.
Its going to take time(if they stick with it), but if Germany continues to arm it self, I wouldn't be surprised if they become the new European superpower, maybe they just need Nuclear weapons at the end to seal the deal?(although I really doubt this will go down well with the population).
UK as a full, voting member of the EU, on request? Not going to happen any time soon. Far too many downsides from the crazy brits. The UK would have to prove to the EU that they are going to be constructive, have worked all of the Brexit insanity out of their system and it wasn't coming back. This might take a while.
UK as an "EU aligned rule-taker" that participates in the single market, without voting rights, a bit like Norway? Sure, that's an easy win for both parties.
No, the UK won't have any voting power as a full member in the EU for quite a while, the EU will not allow that soon. 5-10 years seems optimistic IMHO.