You believe that being an EU member prevented having the "massive benefit to both parties" in the past? Is it not more likely that a government that has publicly committed to reducing immigration was not interested in such benefits if indeed they existed?

Firstly, that’s a different point. You compared an immigration policy with sovereignty or the ability to make law in a different state.

Since you want to move the goalposts, yes, the public was and is interested in reducing overall immigration, especially of low skill. Even if it wasn’t, you appear to be suggesting that any immigration would be opposed, especially from India. Not sure where you get that idea from.