Where I live in Surrey, some state primaries have a good number of children applying to Independnet senior schools. They do write references but they aren't as detailed as the Prep schools write. The smaller schools which have fewer reference requests tend to just do them, but for some if the larger primaries/Juniors, the number if reference requests are significant and a drain on teacher time, so they charge £25 (last I heard anyway). It doesn't strike me as entirely unreasonable to be honest.
And I would agree that state school references aren't going to be the determining factor in an application progressing unless some serious behavioural issue is highlighted or something else really significant. The Senior schools are interested to see things like CAT scores which lots of Preps have done, but primaries haven't usually. The entrance exam will count for far more than the reference in most cases and lots of primary children get into highly selective schools, often with a bit if tutoring,mbut then lots of the Prep kids are being tutored too.
If you're looking at the independent sector, you just have to get used to paying for things.....you pay an application fee and if you need to pay for a reference, just see it as part of the cost of applying. I would be shocked if a school point blank refused to supply even a brief reference, and I have never heard of that round here to be honest.
If however, only a skimpy reference is provided, really don't worry - the Senior won't be overly surprised and knows that some Primary Heads are ideologically opposed, and will take more note if the entrance exam.
In the end, entrance exams are the big deal. References and interviews are usually just to confirm what is already thought and to highlight anything very unusual and also to allow schools to justify their choices not purely on academics, but to have whoever they like.