report, almost 40 per cent of "town and country" constituencies are in the bottom 25 per cent of results. Some 30 per cent of countryside constituencies are also in the bottom quarter.
In contrast, no London constituency and just 20 per cent of other major urban constituencies are in the bottom 25 per cent. Overall, the South East and East of England have the worst results.
The study has been published as part of Save the Children's Read On, Get On campaign, which aims to get all children "reading well" by the end of primary school.
Gareth Jenkins, director of UK poverty at the charity, said: "Read On, Get On is a crucial mission to get all children reading well but this can't happen while poor children are being forgotten, especially in the Home Counties, coasts and towns.
"This report shows that no area in England is currently meeting the Read On, Get On goal of getting all children reading well at 11. And this is a problem because being unable to read well has dismal consequences for a child's future, preventing them from passing exams and finding jobs, and locking them into a lifetime of poverty."
Most areas have shown improvements in the reading ability of low-income pupils, but in 35 constituencies - including Leeds North East, Wokingham in Berkshire and South Leicestershire - students are performing worse than they were 10 years ago.
Other constituencies identified as being among the bottom 25 per cent for poor children include Maidstone and the Weald, Ipswich, Berwick-upon-Tweed and Daventry.
Jonathan Douglas, director of the National Literacy Trust, which is part of the Read On, Get On coalition, said: "Identifying those children who are falling behind is a crucial step in our national mission on reading. It is simply unacceptable that we allow poorer children in high-income areas to fall behind.
"We know from our experience of supporting disadvantaged children's literacy just how important a tailored local approach is - and that schools, parents, businesses and community partners all have a vital role to play."
The Read On, Get On campaign was launched in September by a coalition of children's charities, businesses and educationalists. Its aim is that, by 2025, all children leaving primary school will be able to read well, which is defined as reaching national curriculum level 4b and being able to read and understand a range of different books, magazines and newspapers. Campaigners have called for politicians and parents, as well as the education profession, to back the initiative.
Many explanations have been given for the success of London's schools. The most recent, from the University of Bristol, is that the city attracts migrants with high hopes for their children and that schools are more integrated than elsewhere.
Save the Children's report comes after the Social Mobility and Child Poverty Commission pointed out last month that a disproportionate number of schools that performed relatively poorly for disadvantaged students were found in the South East. It said that getting the best teachers to teach in the worst schools would require stronger incentives, including higher pay.
`Teachers are aware'
Tim Eastwel is headteacher of Lincewood Primary School in Basildon. In 2014, 95 per cent of his students receiving pupil premium funding reached level 4 in reading - the same proportion as their non-pupil premium classmates. Progress in reading was also identical for both groups.
"We identify these children as soon as they come into school," Mr Eastwell says. "We have tracking meetings every half term, when we look at individuals and make sure we put in place what they need. That might be differentiated work in classes, additional interventions or one-to-one tuition.
"It is about teachers being a lot more aware of who those pupil premium children are, but treating them, and any children who are falling behind, as individuals."