Ninety primary schools in England have been forced to reduce their catchment areas to just 300 metres, meaning children living further away are likely to be refused a place, according to a report.
Parents moving closer to their desired school in the hope of securing a place for their children and Britain's growing population have contributed to the situation.
Data from the online service FindASchool shows the smallest catchment area is in Fox Primary School in Notting Hill, west London, at just 92 metres.
The report in the Times has been published the day before the deadline for parents of four-year-olds to apply for a September 2016 primary school place.
Ed Rushton, founder of FindASchool, a new service from 192.com, told the newspaper: "Forty-six per cent of schools in England and two-thirds of schools in Greater London are oversubscribed - all of the schools are filling up whether good or bad.
"It's slightly farcical to talk about having a choice. You get what is allocated. Getting your sixth choice is not really a chosen school."
Thousands of families are expected to miss out on their first-choice place, as in previous years.
The New Schools Network has also released figures which show that many schools had more than three times the number of first preferences as places available.
According to The Times, the average cut-off distance for all oversubscribed primary schools in England is 2.3km (1.4 miles).
However, on FindASchool, 90 schools offered no places for youngsters living outside the 300-metre catchment area. According to the Times, this included three in Birmingham, three in Manchester, four in Bradford, four in Kent, two in Plymouth, two in Gloucestershire and 39 in London.
A Department for Education spokesman said: "We want every parent to have access to a good school place for their child. Despite rising pupil numbers, 95% of parents received an offer at one of their top three preferred schools last year.
"We doubled basic need funding for new school places to £5 billion between 2011 and 2015, which helped to create half a million new school places since May 2010. This helped to correct the decline of over 200,000 places between 2004 and 2010.
"To ensure parents continue to have a choice, we are investing £23 billion in school buildings up to 2021, creating 500 new schools, and 600,000 new school places. This comes after we changed the rules to make it easier for good schools to expand."