There are a couple of schools in my town that have separate infants and juniors. Mist kids in the infants go straight through to the associated junior school but they also have new applicants at junior stage because the classes are slighter larger (the ones in my town).
The school I used to go to was a JMI school, it changed sometime between the 2000 and 2006 OFSTED inspections, but it's still sometimes referred to as Xvillage JMI in parish newsletters. It operated as a straight-through primary, though, with no new application needed for y3.
The school I currently work at is a Junior school which you do have to apply for - the associated infant school is a separate school with a different head and Governing body. There are several schools in the town which have fairly recently amalgamated separate infant and junior schools to become straight- through primaries, and others where the two are federated, either with a joint governing body or with different governors but one executive head overseeing both schools.
It's a dated term for a mainstream primary school where infants and junior sections are on the same site but in separate buildings or sections of the building.
Initially JMI schools were in contrast to the traditional system of having mixed infants' schools but separate junior schools for girls and boys - you can still see this on lots of Victorian primary schools in London, which have separate entrances for girls and boys. So JMI was a way of indicating that a school had amalgamated the girls and boys' sections of the junior school.
IT's pretty much redundant as a term now that single-sex primary schools are pretty much obsolete in the state sector, but some schools still retain it as part of their official name.