20% 'miss primary school choice'
Up to one in five infants in some parts of England are missing out on their top choice of primary school.
In parts of London this rose to more than a quarter.
Data from the Hertfordshire council shows that 81% of youngsters have got their first preference.
London Councils also said that 80.97% of pupils got in their first preference school in the capital - where a record 103,387 applications for places were made.
There were wide differences around the country, with up to one in six missing out on their first preference in some areas, compared with almost all getting their number one pick in others.
A continuing squeeze on places, particularly at primary level - fuelled in part by a rising birth rate in recent years, combined with the effect of immigration in some areas - means that some parts of England are struggling to accommodate every child.
Helen Jenner, chair of the Pan London Admissions Board, claimed: "The fact that 81% of pupils have been offered their first preference, even though boroughs received 900 more applications this year, reflects how proficient the London system is at matching places with pupils."
London has seen the school-age population increase at twice the rate of any other region in recent years and 99,059 applicants got a place at a school of their preference this year, compared to 97,958 last year.
Successful first preference picks in London ranged from 58.99% in Kensington and Chelsea, 73.86% in Hammersmith and Fulham, 75.01% in Camden through to 90.64% in Barking & Dagenham.
Ms Jenner warned: "As London's pupil population continues to grow, creating more places will become increasingly difficult."
Ahead of what is known as National Offer Day, Labour released new figures which it claimed showed that a growing crisis in school places means that more than 100,000 five to seven-year-olds are being taught in "supersize" classes".
The party said its analysis of data obtained from freedom of information requests to local councils reveals that the numbers of young children being taught in classes of more than 30 pupils has reached its highest level for 15 years.
It blamed the rise on the Conservative Party, which it said had spent millions on setting up free schools rather than focusing funding on areas in need of more places.
Initial results from a Press Association survey of town halls shows that families in some areas are more likely to gain a place at their top choice than in others.
In Kirklees, 90.4% of youngsters have got their first place, with 90% in Oldham.
Results from Birmingham show that 84.7% of children starting reception have got their first preference, while 94.8% got one of their listed choices. Around 5.2% - 826 children -- were given a school that was not one of their preferred options, while a further 3.3% - 532 youngsters - have been offered a school outside the city.
Figures from East Sussex show that 84.68% got their first choice, while in Southampton the percentage was 85.4%.
Other early results include Derbyshire, where 93.4% of youngsters have their first pick, Torbay was 86.2%, Bristol was 84%, up from 82% last year, and Cornwall was 90.7%.
The survey results show a mixed picture, while some areas have seen a rise in youngsters gaining their top choice, others have seen a drop.
Southend has seen a 3% rise, with 87% of infants offered their first preference, up from 84% last year, while Hull has seen a rise from 89.34% in 2014 to 92.04% this year.
But Stoke has seen a fall, with 89% of youngsters getting their first choice for this September, compared to 92.2% last year, and in Wokingham first choice offers have dropped one percentage point to 85%.
Russell Hobby, general secretary of the National Association of Head Teachers (NAHT), said: "Since 2011, the powers of local authorities in planning school places have been significantly reduced without an alternative system to take their place.
"We have a Balkanised system, with authorities, academies and central government taking decisions in isolation."
With the massive increase in pupil numbers and overstretched budgets, now is not the time for inefficiency and conflict, he claimed.
Last week, town hall chiefs warned that more than half of areas could have more primary school pupils than there are places available in just two years' time.
The Local Government Association (LGA) said its analysis of official figures indicates that by September next year, two in five local authorities in England - 66 out of 152 - will have more children ready to start school than there are places.
It claimed that by 2017/18 this will increase to more than half (85 areas) and go up to three in five dealing with more pupils than places (94 areas) in 2018/19.
Findings from the National Foundation for Educational Research (NFER) show that three-quarters of parents felt they had a genuine choice.
Household income and local factors were the most important influences, according to 1,005 parents of children aged five to 18 in England who were questioned in December 2014 and January 2015.