Just like Anti-Brexit leftist in the UK.
The people have already voted for change. It’s best to deliver what they expect, or else.
No, not quite, and the difference (for us) is very important.
The People of the UK do not make laws, not even indirectly. Laws in the UK, except for 1649-1660, are made by the Crown in Parliament, so although you could argue if you believe in democracy that the Crown in Parliament has some kind of moral duty to pass a Brexit law, they are not bound to do so.
Laws in the US are made by the People, indirectly, acting through a Congress to which certain powers of the People have been delegated while others have been retained.
So, the US immigration laws belong to the People, while the UK immigration system is a free grant of the Crown in Parliament.