Close ties between the UK and the EU is of interest to both parties. However, there’s a very loud minority of the UK populace supported by a lot of the right wing press, who will have a hissy fit if the government shows any indication of collaborating with the EU.

Therefore what your suggesting just isn’t possible. What is possible is a bespoke deal. It doesn’t have to provide unique benefits, that other countries don’t enjoy, it just has to be labelled sufficiently different to quash the overreaction of the right.

Basically, it has to be “special” and “privileged” but only in the sense of wrapping right wing snowflakes in cotton wool. In reality it’ll be a worse deal than the UK once enjoyed, and worse than if the UK rejoined, but at least it would be better than the fuck all we have now.