Priti Patel has apologised for the time it has taken for Ukrainian refugees to arrive in the UK under two visa schemes, after new figures showed just 12,000 have so far reached Britain.

While other European countries have accepted hundreds of thousands of people fleeing the Russian invasion, only about 1,200 people have so far arrived in Britain under the Homes for Ukraine scheme for those who are sponsored by UK hosts. Another 10,800 have arrived under the Ukrainian family scheme for those with existing family connections to the UK.

The figures show that by Thursday, the government had received 79,800 visa applications from Ukrainians for visas and had so far issued a total of 40,900 visas.

In a pre-recorded interview with the BBC, Patel said: “I apologise with frustration myself … it takes time to start up a new route.”

She said it was “always easy to blame someone else” but security checks were “not the problem” when it came to the time it was taking for Ukrainian refugees to reach the UK.

Her words prompted an angry response from British hosts who say the government’s insistence that Ukrainians apply for visas is causing anguish and has left some out of pocket after paying overseas hotel bills for delayed refugees.

Lauren Corbishley, a mental health nurse who has been waiting 21 days for the government to issue visas to a Ukrainian family in Poland, said: “Priti Patel’s apology is an insult to those thousands of people like me who are waiting to hear or receive their permission to travel letters. Empty words.

“We are still financially funding my family in Poland and there is no end in sight. I was a Tory voter once upon a time, however after this visa scandal and the way I have been treated along with many others will not vote again for this appalling party.”

Kelly Bibb, an event manager, has sponsored a psychiatrist from Kyiv and two daughters, who are staying in a village in western Ukraine while they await their visas. Several families in her village in Hertfordshire applied to sponsor 11 refugees, on 23 March, and just one visa has been issued so far.

Her house has been inspected by the local council, the DBS checks are under way, and school places have been organised. When she asked her MP to make inquiries about the delay, she was told some of the data was missing and the refugees’ passports needed to be uploaded again.

“I feel ashamed and embarrassed that it is taking so long. They’re safe at the moment, but they are still in Ukraine. The system is a shambles,” she said.

One refugee charity has called on the government to urgently review the use of visas and waive them as an immediate short-term measure.

Enver Solomon, the chief executive of the Refugee Council, said: “The visa schemes are entirely unfit for purpose in responding to the biggest refugee crisis in Europe for a generation.

“Asking Ukrainian families, who are scared, exhausted and traumatised to fill out a long and complex application is unacceptable and totally out of touch with the terrifying situation they find themselves in.

“By choosing control over compassion when it comes to granting refugees protection the government is out of step, not only with … the British public, but the rest of Europe who have opened their doors to welcome tens of thousands of Ukrainian families in desperate need,” he said.

Homes for Ukraine launched on 14 March. Its aim is to allow individuals, charities, community groups and other organisations to sponsor named refugees, housing them in their homes or buildings.

Those who do not personally know someone fleeing Ukraine have been advised to contact groups who are starting to make connections between individuals, to match them to a refugee.

The UK requires refugees to have a visa before they enter, unlike other European countries which have waived the checks to speed things up. Those who are granted a visa under the scheme will be eligible to work, and can access state benefits and public services for three years.

As of Thursday, 12,500 visas had been issued under the sponsorship scheme out of 43,600 applications, according to the Home Office figures. Out of 36,300 applications for family visas, 28,500 have been granted.

The quickest way to help Ukrainian refugees would be for the UK to stop requiring visas for those fleeing Ukraine, which would bring it in line with many other countries that have done so since the crisis began, said the British Red Cross.

Refugees with a valid Ukrainian international passport can apply online, but those without one have to go to a visa application centre. The Home Office minister Richard Harrington said approximately 10% of applications so far were from people who were having to go to the centres.

After being told by the BBC there was “huge frustration” among the public who were experiencing three- to four-week delays and were blaming red tape for being unable to put people up, Patel replied: “They’re not seeing delays. We are processing and, as I’ve said as well, I’m streamlining processes.

“I streamlined the family scheme in less than a week, and we simplified that and we changed the way certain checks are done. Also, I’m working to automate where we can.”

Asked why Britain was playing “catch-up” with other countries, Patel said comparisons with EU members were not “like for like”.

A government spokesperson said: “Applications are normally processed in date order from when applicant documents are uploaded. The Home Office is aware some applicants have been waiting nearly three weeks for their applications to be progressed or an outcome to be communicated.

“We acknowledge that this is unacceptable and we are working to resolve this and continue to speed up the processing of applications.”

A government source said it had been “a victim of the popularity of the scheme”.

“We’re not yet in a situation where we have anything like the turnaround time for visas that we’d like to have or indeed that we’d been led to believe that we would be able to have.”

An email was due to be sent out to all those who had applied, making it clear that it might still be some time before the visas were processed, because of the large numbers who had applied.

The government has noted that the number of people who have arrived in the UK is less than the number of visas issued. Government sources have suggested that may mean some people are applying to the UK as one of a number of options.

However, people who have applied have noted that because visas are issued to individuals rather than to family units, it is usually not possible to travel until everyone has been granted a visa, and there have been large gaps between issuing dates.