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I would bet that identity cards have to be back on the table.
For any measure of control over immigration, benefits, fraud, etc... there's going to have be a moment where the government figures out how to force a real count. A census isn't enough, it's got to be a real count, and kept accurate and up to date going forward.
I imagine that they could re-purpose the benefits system to lay the foundation of that. They already have parts of it... this is your card, without it you cannot claim, you must present it each time, etc.
The only way to have such a system be complete, and current, is to make it a part of life. Opening a bank account? Need your card. Claiming a pension? Need your card. Going to a hospital for a non-emergency? Need you card.
It'll be voluntary, until it's so pervasive that it can't be voluntary.
I'm not actually against an identity card, they work well in Sweden, Germany, etc. So long as they serve the people, they can be great. But of course, this is the UK, and we tend to make systems that serve governments and authority, not the people.
But yeah... I wouldn't read track record into anything. Brexit is an opportunity, the largest ever presented to a UK government (even superceding the end of WW2 as we have wealth and means now)... to reshape the country, constitution, institutions.
The Conservatives are not going to waste that chance, and it's a strong justification for moving fairly quickly (before the next general election) to define this and set it in motion.
Ultimately though, it's a boiling frog problem. How much can they get away with whilst keeping unity within the party and protecting their slim majority.
https://en.wikipedia.org/wiki/David_Davis_%28British_politician%29
So this guy has to negotiate the exit. Strange mix of imho sensible views on identity cards/child benefit/EHRC with not for LGBT rights/likes capital punishment.
Unless he's changed his tune on those by now.