

Any significantly stronger ties required Freedom Of Movement (basically to be inside the Single Market, even as a non-EU-member, means having all rules necessary for it to be a free and open market, which includes Freedom Of Movement), which was one of the main reasons the Brexiters won - like in the US now, Britain’s very own rise of the Far-Right by taking over their mainstream conservative party some years ago was also mainly anchored on racism.
I’m quite curious how many of those 66% of Britons would still be alright with stronger EU ties if that meant that Poles could once again immigrate to Britain at will.
There are ways to be part of the Single Market and all that goes with it without becoming an EU member, for example by becoming a member of the EEA like Norway.
They would be able to keep the Pound that way, as well as a number of other things such as controlling the fishing rights in their own waters.
They would however have to accept Freedom Of Movement, which was one of the main arguments for Leave during a Referendum which was very much a mix of racism and fantastical expectations of keeping most of the rights even after leaving the EU (Britain has major problems with widespread nationalistic delusions of grandeurs, so lots of people believed all the fantasies about “they will give us all we want”)