The proposals stem originally from the Tower Hamlets Mayoral Election of 2014 where voter fraud (both in person and postal) was so massive that the whole election was declared void and had to be re-run.
It is the independent Electoral Commission, not the Tories, who proposed 3 requirements to prevent electoral fraud. Voter ID was the third of these, and if Labour had won in 2015, 2017 or 2019 they would have had no choice but to pass a law for its introduction. Labour might have come up with a different list of valid IDs but the law would have been substantially the same.
FYI. The first electoral change was introduction of individual electoral registration instead of one person doing it for the whole household. The second was a ban on parties and their campaigners handling postal and proxy vote applications.
Proven cases of voter fraud are low, even the Tower Hamlets fiasco in 2014 resulted in no criminal prosecutions, but suspected cases are not insignificant. Talk to people who work in polling stations and they will tell of one person turning up with 6 voting cards expecting to be given 6 ballot papers. I have heard of a person handing in a voting card who staff were sure had already voted earlier, but there is nothing they could do about it (especially when the person voluntarily showed supporting ID for the suspected second vote). They may have observed a "leader" of some sort directing "followers" exactly where to put their crosses. They may have seen cases of people voting with an apparently legitimate polling card who they suspect lives in a neighbouring borough and may also have voted there.
The rules for postal votes are also due to be tightened, but it was left out of this Voter ID legislation - it may come later. Proposals include tightening up ID checks, introducing online applications, and much tighter restrictions on who can hand in postal votes at polling stations (where it is too late to post the ballot paper). One of the main proposals that people will need to re-apply every few years (2-4?) for a postal vote. Currently, if you apply for a postal vote, you effectively have one for life.