Thousands of families in England have failed to secure a place for their child in their first choice of primary school amid continuing high demand in London, Birmingham and other hotspots across the country.

While schools remain largely closed because of the Covid-19 pandemic, families across the country received emails on national primary offer day on Thursday, informing them which school their child will go to in September.

After a spike in the birthrate beginning in the early 2000s, there has been a gradual flattening in the number of four- and five-year-olds enrolling in primary school. But some local authorities reported an increase in applications this year and a fall in the proportion of children getting into their first-choice school.

Competition for places remains intense in London, where applications have increased, reversing last year’s trend. Of the 97,300 pupils who applied for a primary school place in the capital, less than 85% got into their first choice, down from 86% last year, and 5,000 children did not get into any of their top three schools.

Birmingham also experienced an increase in applications, taking the total to more than 14,400, which has had a similar effect on the success rate of applications. The percentage of families getting their first choice slipped from 89% last year to just under 88%.

For families wishing to appeal, the Department for Education has announced plans to temporarily relax regulations so that hearings can go ahead despite the Covid-19 restrictions. They will no longer need to be attended in person.

Richard Long, Kent county council’s cabinet member for education and skills, said: “Since the partial closure of all our schools last month, everyone involved in the provision of education has … been working in challenging circumstances, and it is a credit to them that we are still able to release offers today.”

In Kent, where primary schools will welcome almost 18,000 pupils in September – their biggest cohort in four years – just over 88% gained a place in their top choice, 97% got into one of their three preferred schools, and just over 450 did not get any of their preferences.

Long said: “I appreciate that for those families who did not receive one of their preferences there will be feelings of disappointment and concern today. I would like to reassure them that this is just the first stage of the application process.

“Families have the option to appeal or join a waiting list for an alternative school if they are not happy with their allocation and there is likely to be considerable movement between now and September as families do not take up places they are offered.”

Devon also saw a big jump in the number of families applying for a place in reception this September, with more than 7,500 applications, up 300 on last year. Almost 95% of families got their first preference and 98% got into one of their top three.

In York, the percentage of families given their first choice fell from 96% last year to 94%; in Reading, Berkshire, 83% of children got their first preference, while in nearby Wokingham, 85% got their top choice, also a drop on 2019.

In Manchester, where there has previously been high demand, applications fell from 7,057 last year to 6,921. As a result, 92.1% of families got their first choice compared with 90.9% in 2019, and 97.8% of applicants got one of their top three choices, up from 97.2% last year.

Just over 97% of families in the East Riding of Yorkshire got their first pick, in Derbyshire it was 95%, and in Wiltshire 94%. In contrast, in London’s Kensington and Chelsea, the figure dropped to 70%, in Hammersmith and Fulham it was 73% and in Camden 75%.

Gail Tolley, spokesperson for the Pan-London Admissions Board and strategic lead for children and young people at Brent Council, said: “Coordinating more than 97,000 applications to primary schools across 32 London boroughs and the City of London Corporation is always a complex task – and this year the coronavirus pandemic has put even more pressure on boroughs.

“Thanks to the hard work of our admissions teams, we can reassure families that the process has gone smoothly and the vast majority of children – 97% – will receive an offer for a reception place at one of their preferred schools.”

In 2019, 90.6% of pupils were offered their first choice of primary school and 97.5% of pupils were offered one of their top three.