Children who are not hitting standard targets at 4 are not failing to hit the targets because of poor teaching - it will more likely be either a noneducational home background, or innate learning difficulties - those same children are going to be the ones who are not hitting standard targets at 11. But teaching cannot affect home background, and can only to a certain extent affect the impact of innate learning difficulties - so how are these teachers supposed to turn these children into 'achievers'?
I do understand your dilemma about the underachieving school, actually, because ds1 goes to one. The percentage of 11 year olds hitting the government target for English was 20% lower than any other school in the area ... the school has poor parental support. But then you have to factor in things like the percentage of children with special needs who were taking those test - parents of children with special needs deliberately send their children to what is, on paper, a failing school, because it has the most experience and the highest calibre of early years and SEN teaching staff - it has to have.
Typically each classroom is 30% special needs. It is a lesson of inclusion at work - ds1 is making leaps at school - but on paper, the school is awful.
Were they to take a sample of a typical for another school range of learning abilities, they may find the standard test results a little more comparable, and the same may be true of your local school.
A race is only fair if everyone has the same distance to run. Some schools are 50m behind everyone else.