More Ukrainians will be allowed to enter the UK to join family members as they flee the war zone, Boris Johnson announced.

The Government has been criticised by Tory and opposition MPs for the response to the refugee crisis, but the Prime Minister insisted the widened access would allow “very considerable numbers” of Ukrainians to come.

A new scheme will also allow individuals and organisations to sponsor Ukrainian refugees to come to the UK.

The first phase of the plan had allowed people in Ukraine who had immediate family members in the UK to come and join them, but the move was criticised for being too restrictive.

On a visit to Poland – where refugees have been crossing the border from Ukraine following the Russian invasion – Mr Johnson promised to do more.

He told his Polish counterpart Mateusz Morawiecki: “We stand ready, clearly, to take Ukrainian refugees in our own country, working with you, in considerable numbers, as we always have done and always will.”

Downing Street said people living in the UK would now be allowed to bring in “adult parents, grandparents, children over 18 and siblings” in addition to those who had previously been allowed.

The Prime Minister’s official spokesman said that would widen eligibility to around 200,000 people, twice the number previously estimated.

Mr Johnson said later: “What we are going to do is we are extending the family scheme so that actually very considerable numbers would be eligible … you could be talking about a couple of hundred thousand, maybe more.

“Additionally, we are going to have a humanitarian scheme and then a scheme by which UK companies and citizens can sponsor individual Ukrainians to come to the UK.”

The UN’s refugee agency says that about 660,000 people have fled Ukraine for neighbouring countries since the Russian invasion began.

Shabia Mantoo, a spokeswoman for the UN High Commissioner for Refugees, said: “At this rate, the situation looks set to become Europe’s largest refugee crisis this century.”

Giving more details of the UK’s visa schemes, Home Secretary Priti Patel called for a “national effort” to offer sanctuary.

She told MPs both the family route and sponsorship route would allow Ukrainians to reside in the UK for an initial period of 12 months.

She said the sponsorship scheme would “open up a route to the UK for Ukrainians who may not have family ties with the UK but who are able to match with individuals, charities, businesses and community groups”.

Ms Patel said: “This is a very generous and it is an expansive and unprecedented package.

“It will mean that the British public and the Ukrainian diaspora can support displaced Ukrainians in the UK until they are able to return to a free and a sovereign Ukraine.”

Shadow home secretary Yvette Cooper welcomed the changes but questioned Ms Patel over whether more could still be done.

“Does the sponsoring family member have to be British or have indefinite leave to remain? What about Ukrainians here on work visas, on study visas, who have come maybe as lorry drivers or on visitor visas?

“Surely she is not expecting to turn their families away? When people are fleeing Russian authoritarianism or war I assume she will not be applying a test based on which bureaucratic box UK residents tick.”