The Government expects the number of Ukrainians being granted visas for the UK to increase “very, very quickly”, a minister has said.

The Home Office has been under pressure to do more to help people feeing the war after it revealed on Sunday that only “around 50” visas had been issued under the Ukraine Family Scheme as of 10am that morning.

Foreign Affairs Committee chairman Tom Tugendhat, said the rate was “certainly not a success”, while shadow home secretary Yvette Cooper tweeted: “This is too slow.”

Prime Minister Boris Johnson was unable to provide the latest figures on Monday but told reporters: “We’re processing thousands right now.”

The Home Office refused to disclose fresh figures, with a spokeswoman saying the department would not be providing a “running commentary”.

It was reported on Sunday that Home Secretary Priti Patel is examining “legal options” to create a “humanitarian route”, which would offer all Ukrainian refugees the right to come to the UK, regardless of whether they have family ties here.

But it was unclear whether this referred to a sponsorship scheme that has already been announced, with Europe minister James Cleverly saying on Monday that there had been no change to the plans over the weekend.

Speaking to Sky News on Monday morning, Mr Cleverly said the Government has made it “absolutely clear” it wants to support Ukrainians seeking refuge.

He acknowledged that “only small numbers have come so far” but “the process has only just started”.

Mr Cleverly also told LBC that the number of Ukrainians being granted visas for the UK will increase “very, very quickly” but the scale of the crisis is “unprecedented”.

“This is the largest refugee flow that we have seen since the Second World War,” he said.

The Home Office “had to create a system pretty much from scratch”, he said, and the process “will get quicker and slicker and faster”.

“It will take a little time to get the system up and running, that’s now there, I have no doubt that the numbers will start coming through,” he said.

Ms Patel said over the weekend that the UK is “doing everything possible” to speed up efforts to grant visas to Ukrainian refugees, and told the Sun she is examining a “humanitarian route” to allow all those fleeing the conflict to come to the UK.

But it is unclear whether this “humanitarian route” is actually a new concept, or refers to a sponsorship scheme already announced – whereby individuals and organisations will be able to bring Ukrainians to the UK.

Ms Patel told the newspaper: “In response to the desperation I saw with my own eyes at the Polish border two days ago, I’m urgently escalating our response to the growing humanitarian crisis.

“I am now investigating the legal options to create a humanitarian route.

“This means anyone without ties to the UK fleeing the conflict in Ukraine will have a right to come to this nation.”

Mr Cleverly told BBC Breakfast on Monday: “We’ve got two routes by which Ukrainians can come to the UK.

“One is where they have family connections, but we also have a broader humanitarian route for Ukrainians who do not have family who are already here in the UK – there is no particular target or limit on that route.”

Asked whether there had been a change to the plans over the weekend, he said: “No, no, no. This is what’s been in place previously.”

Later, Downing Street confirmed the “humanitarian route” reportedly being examined by the Home Secretary was in fact a sponsorship scheme that had already been announced by the Government.

A Downing Street spokesman told reporters: “It’s the sponsorship route that we set out last week.”

He added: “We’ve set out the details of the two routes that we are putting in place to help those displaced Ukrainians who would like to come to the UK.

“We will set out more details this week around the sponsorship scheme, which as I say will provide a route for Ukrainians without any family ties to the UK – and there is no limit to that scheme. That will welcome as many Ukrainians as wish to come and that have matched sponsors.”

The Home Office was unable to confirm if it was working on drawing up additional measures for Ukrainians to come to the UK, but a spokeswoman said: “This is a rapidly moving and complex picture and as the situation develops we will continue to keep our support under constant review.”

Mr Johnson said the Government would not introduce a system whereby Ukrainian refugees can come to the UK “without any checks or any controls at all”.