We had ID cards during WW2.
On February 21st, 1952, Churchill's new Conservative government, which had campaigned under the slogan "Set the people free," abolished National Identity Cards as part of a campaign against regulations and controls.
The cards had been introduced in 1939 as a wartime measure, anticipating the dislocation of the population that would be caused by mobilization and mass evacuation. The postwar Labour government retained them, citing their need for National Service registration, rationing, the Health Service, family allowances, and post-war credits. Post Office clerks who were uncertain of a customer's identity, could demand to see them.
The police fell into the habit of demanding to see them, even for trivial matters such as overstaying one's time in a parking slot. There was a widespread feeling, expressed in Parliament, that this was un-British, and was more redolent of the practices of totalitarian countries. A famous test case aided those campaigning for repeal.
When Clarence Willcock, a dry cleaning manager, was stopped on suspicion of speeding, the police demanded to see his ID card. He refused on principle, and was convicted and fined at a magistrate's court. He took the case to the Court of Appeal, and although the judgement against him was upheld, Lord Chief Justice Lord Goddard commented that the Act was intended for emergency uses, now over, and should not be invoked on trivial matters. He further remarked that demanding production of the card for its own sake tended “to turn law-abiding subjects into lawbreakers, which is a most undesirable state of affairs."
I see no evidence that we wouldn't get similar levels of petty criminalisation if they were reintroduced.