Does China have a trade agreement with the EU?
Do they have a freedom of movement agreement as well?
China isn't a valid comparison. They're massive, and they're not divorcing the EU, so the terms of negotiation are in a completely different ballpark. Same as the USA/EU.
We'd be joining the EFTA. We're a part of the European continent. If the EU let us do anything other than that, they'd be opening the floodgates for countries leaving. Not going to happen.