My DS has been at private school since he was 4 (in Scotland), and just started Senior School.
Local Senior schools where I live really aren't great, so I made the decision to send him from P1, so he would go all the way through his schooling at the same school.
The entrance test is simply to see if there are any glaring difficulties that they may need to be aware of before they start, and also if the age dictates that they may be able to defer for a year, whether that would be appropriate.
I don't have any experience of local primary schools, but DS flourished, in P1, there was only 12 in his class, and because his school goes all the way up to age 18, they were able to access teachers from Senior School for specialist subjects. There was so many extra-curricular activities & he found a few that he absolutely loved.
Our NDN is the same age as my DS & goes to the local primary school, and he & his friends seem to be less mature than my DS & his friends from school, and he had a really hard time transitioning up to Senior school, however my DS found it really easy as there was really no change at all (same building, same uniform, same friends, same timetabled subjects)
There is a huge mixture of children, because by law, they have to offer scholarships.
In DS's class there was one dyslexic girl, and one boy with autism, because of the small class sizes & availability of teaching staff, essentially had one on one teaching for the first 4 years.
However, all of the "extras" really do add up. Uniform is very specific & not cheap (£25 for shorts/trousers, £60 for a tracksuit), and they have to have specific kit for different sports (rugby, hocket, cricket), plus stationery & books.
I wouldn't change the decision I made, but I may have made a different decision if the local Senior School was better.