Even so, demography is destiny. Europe is toast. Very many Mohammeds are getting to be voting age and they have EU ids.
With regard to voter ID, the system is curiously reversed. Each council maintains an electoral register, basically a list of all the citizens in their area who are eligible to vote. What happens is that several months before an election is called a card drops through your letterbox. This contains a list of all the voters at that address. If the list is right, you can ignore it. If not, you amend it and send it back. They check to make sure the changes are valid and update the register.
The card also details your polling station. Come election day you go along and vote at that station. The staff there have a print out of all the voters registered to their station, and they check your name off against that. You do not need to take the card in.
The culture is that every effort is made to ensure you can vote. In other words, the default position is that they will let you vote. There has to be a good reason for them not to let you do so. If your name is not on the list they have, or your name has already been checked off, then you can still vote, but your voting slip is sealed in a special envelope rather than going straight into the ballot box. The circumstances of the anomoly are written on the envelope and after the polls close it is delivered to the returning officer (the guy who supervises the election) for investigation. If the anomaly is due to some error on their part your vote will be added into the general pool. If it is due to some mistake on your part it gets rejected. If there is evidence of fraud or vote rigging, they call the police in.
In my experience the system works pretty well and returning officers are very thorough in implementing it. As a result, occurences of vote-rigging in the UK are extremely rare. There were suspicions over tampering with postal voting a few years back, but nothing was proven and the system was tightened up in response.