Norway, Switzerland, and Iceland all participate in the EU single market to some degree, without being EU members.

The thing is, you only get the single market proper if you accept freedom of movement. It’s a package deal.

Also, in order to get access to the single market, you have to accept and implement regulations.

Of course, you’ll have to pay for access to the single market, as well, but as a non member have no say on regulations.

Neither of those implications was wanted by the UK.