That is not how most voter fraud occurs. People don't pretend to be other people in the polling booth.
Almost all voter fraud in Britain is done either through misuse of proxy voting, or through harvesting postal votes and either returning them in batches to polling stations on polling day or posting them back. This is why the law is due to change next year so that postal voters will have to reconfirm their postal vote every three years and supply photo id as part of this reconfirmation.
To facilitate this postal vote reconfirmation process, they have had to bring in polling station voting id on polling day too. They have also changed the law on proxy voting too, limiting it to five.
And yes, postal vote tampering and fraud, and misuse of proxy voting, is enough to fix results. In some cases, particularly local elections, you may only need a handful of fraudulent postal votes to return a specific candidate (and that's easily done if you have knowledge and access to a HMO, a care home or a residential home, and filter through the post for people who are no longer in residence, or you are a landlord with a lot of rental properties). I have known a number of cases where it was clear that postal vote harvesting had run into significant numbers.
You can always tell where there is a problem when ballot boxes turn over at verification and they are full of postal votes that have been returned to a polling station on polling day.
It does happen, and, in some areas, it is a serious problem.