Not convinced, you underestimate the actual effect of policies like this. How they are meant to work is one thing, how they actually work in practice is usually quite different.
1. By default, any initiative which seeks to tighten ID requirements is going to cut some people out - otherwise what is the point. The question is how many, and whether it will be the right people.
2. You seem to be assuming that the system will work as described or intended (e.g. if people can have X number of types of ID, then it is all fine). This is not how systems actually work, particularly govt initiatives like this. Usually they fail to work in some way, often quite predictably. As an example, after the tightening of bank rules I have found it consistently difficult to do basic things or make new accounts because my habitation record is non-standard...which started because I was in the Army, and moved every year for 5 years.
2. Is this a problem that needs solving? In America, to listen to the noise, this had become a huge issue even before Trump. However, there is vanishingly little evidence that it is actually a problem: the number of proven voter fraud cases is extraordinarily small (see analysis
here[/url). You can argue that successful fraud goes undetected, but equally I could argue that our elections are being infiltrated by the Illuminati and thetans and Illuminati thetans. Initiatives should generally try to address actual problems, and problems need some evidence that they are a problem. Voter ID policies are quite possibly a solution in search of a problem.
3. Also in America, several studies have found that voter ID laws [url=https://www.theatlantic.com/politics/archive/2017/09/the-trump-voter-fraud-commissions-data-problem/539547/]do suppress minority turnout disproportionately. I suspect that Labour are probably just jumping on that bandwagon by immediately assuming the same is true here, when it is not at all clear that the same effect would happen here because the social system and position of minorities in the UK is very different to black/white issues in much of the US. But it is not a totally unreasonable question to try and answer. Moreover, the more likely effect is that it would suppress voting among poorer and younger people, who are generally more likely to vote Labour, so you can see their interest (and also that of the Conservatives).
I've been refused voting registration several times (for broadly the reasons described in no. 2). My sins are a) I was in the Army, so don't have a 'normal' and consistent habitation and voter registration record, and b) that I work abroad a lot and so have not always been able to turn up in person, or had an address that I could prove I was resident at (e.g. living with girlfriend when in the UK, but my name is not on her household documents). This has even applied, hilariously, to disallowing me from nominating a proxy to vote...when inability to turn up is the whole point of nominating a proxy!
So despite being a citizen since birth, paying taxes in the UK, and having served in the Army, my right to vote has apparently become questionable, because I sit between the boundaries of what the registration system finds easy to understand. People can easily be disenfranchised by these kinds of policies, the question is whether voter fraud is a big enough problem to take that risk. I've seen no evidence that it is.[/url]