The lowest is Knowsley which could fall to zero as the last school teaching A-levels is closing its sixth form.
In a further seven authorities there are less than 20% of students taking A-levels in schools in their boroughs.
Nick Timothy of New Schools Network, which carried out the research, said it was a "glass ceiling" on ambition.
But a Department for Education spokeswoman said the figures were "misleading", because pupils could be studying A-levels in schools in other local authorities.
The analysis shows the wide differences in the numbers of young people taking A-levels in state schools and colleges in their council areas and getting qualifications that would help them apply for university places.
Source: New Schools Network
In 27 authorities, fewer than a quarter of pupils in this age group are taking A-levels in their council area.
In contrast, Harrow has 74% of pupils studying for A-levels in schools in the borough, and it's 71% in Darlington.
Teenagers might be travelling to take A-levels in schools and colleges in neighbouring local authorities.
But the study found that the authorities neighbouring these areas of low A-level take up were themselves likely to have below-average provision, so that students would have to compete for limited numbers of places.
The study warns of a "deep-seated problem" in ensuring that young people in poorer areas are able to take A-levels, saying that "access to A-levels is closely linked to deprivation" - with consequences for higher education and jobs.
But it shows that there is nothing inevitable about poorer areas being linked to low A-level take up and lower levels of university entry.
It highlights St Helens and the London boroughs of Lewisham and Islington as examples of authorities with both higher levels of deprivation and higher levels of young people taking A-levels.
Highest proportion of students taking A-levels
Source: New Schools Network
The analysis has been produced by the New Schools Network, which supports the opening of free schools, and it argues that these cold spots in A-level provision show the need for more schools serving this age group.
"Gaps in A-level provision are creating a glass ceiling for the poorest pupils by limiting access to A-Levels - which still offer the best chance of access to higher education and good employment prospects," said the organisation's director, Nick Timothy.
Leon Riley, who will become head of New College Doncaster, says that it will support students who at present have to go elsewhere.
"Currently 1,200 students travel outside Doncaster to access post-16 education. This cannot be right: we want to make a difference by providing local young people with access to top quality post-16 education," he said.
The analysis by New Schools Network follows the decision by the last school in Knowsley to offer A-levels, Halewood Academy, to close its sixth form.
The authority, which already has the lowest rate of A-level students and one of the lowest university entry rates in the country, will have no one taking A-levels in schools in the borough from next year.
As an academy, Halewood can decide to stop teaching A-levels without the local authority having any powers of intervention.
Parents at the school had campaigned to keep the sixth form, but the academy said that it was not financially viable.
"This is letting down the children of this community. There are people who want to go to university, lots of kids who want to do well," parent Vanessa Pointon said about the closure plans.
Knowsley council says the loss of A-levels in the borough is "not a council decision".
The regional schools commissioner, appointed to oversee academies by the Department for Education, has so far not set out any response to the withdrawal of A-level provision in Knowsley.
The Department for Education has not commented on plans for A-levels in Knowsley, but a spokeswoman rejected the analysis by the New Schools Network.
"These figures are completely misleading - they do not reflect those young people who study A-levels in a neighbouring borough, the actual levels of participation are far higher because many will choose to study in other areas.
"The primary reason the uptake of A-levels differs from area to area is because demand varies across the country. Where there is demand, provision is always available."
The stark regional differences in the proportion of pupils studying A-levels in local state schools in England has been revealed - ranging from 2% to 74%.