Home Secretary Priti Patel has promised a streamlined online visa application system for Ukrainians seeking to flee the war with Russia in response to criticism of her approach to the crisis.

She told MPs the changes will come in from Tuesday following assurances from the security services that the UK can still be protected from Russian efforts to infiltrate the country by posing as Ukrainian refugees.

The Home Office has come under pressure from opposition and Tory MPs – as well as the Ukrainian government – to simplify the system which allows family members of people settled in the UK to join their relatives.

Ms Patel said: “From Tuesday, I can announce that Ukrainians with passports will no longer need to go to a visa application centre to give their biometrics before they come to the UK.

“Instead, once their application has been considered and appropriate checks completed, they will receive direct notification that they’re eligible for the scheme and can come to the UK.

“In short, Ukrainians with passports will be able to get permission to come here fully online from wherever they are and will be able to give their biometrics once in Britain.

“This will mean that visa application centres across Europe can focus their efforts on helping Ukrainians without passports.”

More than two million people have fled Ukraine since Russia’s invasion.

While the European Union allows visa-free travel for Ukrainians fleeing the fighting, the UK insisted they are necessary to guarantee security.

Ms Patel told the Commons: “I am in daily contact with the intelligence and security agencies who are providing me with regular threat assessments.

“What happened in Salisbury showed what (Russian President Vladimir) Putin is willing to do on our soil. It also demonstrated that a small number of people with evil intentions can wreak havoc on our streets.”

Ms Patel said she was able to change the visa regime following security agencies’ fresh advice.

Prime Minister Boris Johnson backed the need for continued checks.

He told reporters: “I think people do understand that when you have got large numbers of people leaving from a war zone – some of them still armed, perhaps not all of their identities completely clear, their motivations completely clear – it is responsible to have checks.”

Shadow home secretary Yvette Cooper, whose urgent question resulted in Ms Patel’s appearance in the Commons, said the Government’s approach had been “shameful”.

The current visa route is restricted to family members of people settled in the UK.

Another promised route, allowing individuals and companies to sponsor Ukrainians to come to the UK, has yet to be established.

Ms Cooper said: “Is this still just being restricted to those with family? Are they still going to have to fill in multiple online forms, or would she now say that all those who want to come to the UK who have fled the fighting in Ukraine can now come here without having to fill in loads of online forms or jump through a whole load of hoops?

“This has just been shameful… making vulnerable people push from pillar to post in their hour of need. Week after week, we have seen this happen.

“It is deeply wrong to leave people in this terrible state. Our country is better than this. If she can’t get this sorted out, frankly she should hand the job over to somebody else who can.”

Figures from Downing Street on Wednesday showed Britain had granted just 957 visas.

Ukrainians have faced a series of bureaucratic hurdles and difficulties in obtaining appointments to complete the necessary paperwork.

Armed forces minister James Heappey said British troops could help in processing claims.

The Ukrainian ambassador to the UK, Vadym Prystaiko, called for an end to the “red tape” restricting refugees from seeking sanctuary in Britain.

He told BBC’s Question Time: “I just wanted to tell you that most of our men are staying behind and fighting, so … most of the people you will see are just women with children, which I totally hope they’re not posing any threat, especially a terrorist threat to the UK.

“So that’s why I hope and I beg that the procedures will be dropped and every bureaucratic red tape should be cancelled.”

Education Secretary Nadhim Zahawi said plans were under way in his department to accept “100,000 children… into our schools”.

It comes as the Home Office disputed claims made by the PCS union about the number of people being deployed to help process Ukraine visas.

On Wednesday, the body which represents civil servants claimed a so-called “surge” team – which the Home Office said it was deploying to Europe to help process applications – only amounted to seven members of staff who volunteered.

A Home Office spokesman said the claims were inaccurate and untrue. The department would not provide an alternative figure or explain why the information would not be made available when asked.

Overall, it is understood hundreds of people are working on the ground and behind the scenes to get visas processed. The Home Office has also taken up Defence Secretary Ben Wallace’s offer of staffing support from the Ministry of Defence.