There were, no doubt, some English people who voted for 'sovereignty, unaware that every international treaty, especially trade deals, involves compromise, not just the Single Market deal. However, the main arguments the spivs and toffs used in 2016 were:
1. It would be better for the NHS.
2. The UK would control its borders better.
3. Immigration would be better controlled.
4. Trade deals would be better.
The sovereignty argument, that the English would be able to make their own laws, was always bottom of the list. This was always the flakiest argument, but the most difficult to refute without giving detailed analysis of all the UK's international commitments. The only significant exercise of sovereignty taken so far is to allow the ruination of English waterways by the foreign owned water companies.
So, brexit has failed to deliver on points 1, 2, 3 & 4, and although a bit of sovereignty has been exercised it is, literally, shit.
Reminder of the leave campaign: http://www.voteleavetakecontrol.org/why_vote_leave.html
Now that all the bunkum about an EU superstate, Turkey joining etc., etc., has also been seen as bogus, and the huge financial hit predicted by the Yellowhammer Report is in full swing, the spivs & toffs can no longer put the blame for their failures on the EU, so they're pinning it on asylum seekers.
Of course, asylum seekers are not exactly popular anywhere in Europe. If the EU brings in tighter restrictions and in turn fewer immigrants make it to England, who will be blamed next?