In the UK, we too have elections administered by professional civil servants according to rules set out in law and guidance from a non-partisan Electoral Commission. Their independence is jealously preserved, and political interference in the process would raise a storm. At the moment there is potentially an issue about Johnson’s government apparently planning to write into law a provision that the EC should come under some sort of ministerial direction, and that there should be a requirement for voter ID, but as things stand:
Registration is a regular annual process (the local authority’s subventions from central government in part depend on the number of voters registered) - it used to be the case that householders were legally required to register all the eligible people in the household, but I don’t know if that still applies since they went to individual registration. The register is available to inspect: the underlying assumption is that local political parties would discover any fraudulent registrations as they canvass, or from general local knowledge, but that rarely happens. On the other hand, it’s a lot of work to fiddle an election, except possibly in local government elections, which is what most such allegations relate to.
Access to polling stations is easy. A central feature here is that the polling district you’re registered in rarely changes, likewise the polling station allocated to it. Each polling district is small enough for the polling station to be in easy distance (I’ve never been further than a few minutes’ walk from mine), and they’re open from early morning till 10pm. Postal votes are easily organised.
Also, electoral boundaries are set by a non-partisan Boundaries Commission. Legislation sets the overall criteria (how many to be elected, what size a constituency should be), but the Commission staff of geographers and the like use the polling districts as basic “building blocks” to try to match the overall criteria to some sense of natural communities.
Also, we don’t have many separate elections on the same day, and if we do, there are separate ballot papers and ballot boxes for each.
Voting is by old-fashioned pencil and paper, which leaves a clear audit trail if a court orders a re-examination because there’s a credible allegation of significant fraud (very rare, and the only case I know was in a very local election). The sealed ballot boxes are taken to a central point, such as a large hall or sports centre for counting. Each is numbered, for another audit trail.
When I was an observer for a candidate, first, the number of papers in each box was counted to confirm it was the same as the number issued. Then the papers from the checked boxes were moved to another table and mixed together, then they were sorted into separate piles for each candidate (each candidate can have a set number of observers, and this is the key part of their job, to make sure their votes don’t go on the wrong pile - but they’re not allowed to speak to the sorters, just to point over their shoulder). Then the piles for each candidate were moved on to the people who counted them into bundles of 100, and the bundles were lined up in trays, with a marker for each 1000. Simple and transparent.