Citizens from other EU member states living in Britain have called on the government to provide more clarity urgently on their status in the event of a sharp end to free movement following a no-deal Brexit.

Although 1 million EU nationals resident in the UK have already applied for settled status, at least a further 2.6 million have yet to apply. More than 100 people in this situation contacted the Guardian on Tuesday to express fears about what their status would be immediately after a no-deal Brexit.

There was profound confusion over the government’s announcement that free movement would end immediately on 31 October, and that a planned transition period would not be implemented.

The Home Office has released a factsheet for EU citizens resident in the UK, reiterating that people have until at least 31 December 2020 to apply for settled status, which allows them to remain in the UK. But many of the questions troubling EU residents remain unanswered.

“Unfortunately this still does not answer the most important question: how will border officials, employers, landlords, the NHS and others distinguish between EU citizens who came to live in the UK before 31 October and those who came after? It leaves people with the impression that the government itself doesn’t know. It simply doesn’t make any sense,” said Stephanie Dawoud of IMIX, an immigration charity supporting EU citizens in the UK.

Many were concerned about making half-term trips, and several said they had cancelled travel plans because they were worried about how they would prove entitlement to return to the UK if free movement ended.

An Australian woman who has dual nationality through her French husband said she was cancelling a trip back to Australia to inter her mother’s ashes. “I am unsure if I will be able to return as I have no proof that I am legally resident,” she wrote.

A solicitor who moved from Sweden at the age of three in the 1980s, who has not yet applied for settled status because she does not have an Android phone, said she was unhappy about having to apply to live in a country she had lived in for decades. The application cannot yet be done on an iPhone, although the Home Office said this will be possible in the autumn, but can be done by post or by going to a dedicated scanning centre, although this takes longer.

Dana Whiston, a German citizen about to move to the UK with her British husband, said she was worried she would be in legal limbo on arrival.

“What will happen if I go abroad on holiday? What distinction is there between me and someone arriving after 31 October if I have no proof of my status? The government is not prepared to answer these questions clearly. They are not interested in giving EU nationals any kind of security. All they want is to be seen to be hard on immigration,” she wrote.

Many people were concerned about how they would prove their entitlement to be in the UK when applying for work, bank accounts or medical care. They were not fully reassured by the Home Office’s statement that they would remain eligible until December 2020.

“What concerns me is what lies ahead, if I am looking for a new place to live in or work at, I am certain that people will ask for proof that I am allowed to live and work here, and a passport won’t be sufficient,” wrote one woman who has not yet applied for settled status.

Pawel Sobocinski, a Polish national who teaches computer science at Southhampton University, said he had decided to emigrate next month to Estonia, where he has found a better-paid teaching job.

“It’s an insult to be asked to apply for settled status after paying taxes for 15 years and teaching thousands of British university students,” he said. “There are lots of reasons why I’m leaving, but Brexit is a big part of it.”

The Home Office said EU citizens and their families should apply to the settled status scheme to avoid possible complications. “However, for those who haven’t applied when free movement ends, they will still have the same entitlements to work, benefits and services and will be able to prove these in the same way as they do now,” the statement said.

Laura Shields, of the British in Europe coalition group, said there was parallel anxiety among British citizens living in Europe over their status. “It has always been about reciprocity. If the EU governments think their nationals are being treated badly, they will act accordingly,” she said.

The Royal College of Midwives also expressed concern over the prospect of a sharp end to freedom of movement. “Well over a thousand midwives working in the NHS are citizens of other EU countries. A great many more EU staff work in hospitals, GP practices and NHS services across the country,” said Gill Walton, the organisation’s general secretary.

“Under these rushed plans, from 11pm on 31 October these NHS midwives, maternity support workers, doctors, nurses and others face an abrupt, cliff-edge change in how they are treated at the UK border.

“They will be viewed with suspicion, even hostility. The plans don’t even make sense. How will a UK border control officer even know which EU citizens are resident in the UK and which are not?”