Yes, the Republican axiom, nowadays stated openly, is that a Democrat is of itself not a legitimate voter, so elections won by Democrats are a definitional matter of fraud.
In your country this really depends on UK particulars that other people sort out and which I prefer you to search out for posting, but based on what we know of the effects of voter ID laws in the US, I would expect limited effects on turnout and Labour vote share from any similar rules if:
1. People without ID are much less likely to be politically active or informed.
2. Affected prospective voters would be disproportionately concentrated in party-locked constituencies.
3. People falling into the target demographic are more politically mixed - when they do try to participate - than those targeting them may assume.
4. Some effects of voter suppression laws can be conditionally compensated for by increased investment in voter outreach and civil-societal or party activism (n.b. this costs money and time).
Sample overview of the American case.
But it's a troubling sign of the Conservative Party's trajectory. I've read that the UK system provides ample time to cast a vote before election deadlines, and that traditional polling places are plentiful with no or minimal wait times. If that's currently the case, worry more if and when the government moves to change it.
I was a little confused to hear this news, because I thought the the UK was counted in the ranks of countries with mandatory universal ID. It turns out Cameron's government reversed the mandate by repealing the Identity Cards Act of 2006 as one of its early actions. Hmmmm...
(If the British government can strictly regulate butter knives, it can hand its citizens ID cards.)
Some tangential data on historical UK election turnout.
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