Boris Johnson today extended Britain's offer of help for Ukrainian refugees after he was blasted for not doing enough.
On Sunday ministers announced some family members of people already settled in the UK could join them from Ukraine.
But only the very closest family members were eligible - excluding grown-up children - prompting furious calls to go further.
Ministers had claimed the scheme could help up to 100,000 people, but this was only a rough estimate of the number potentially eligible - not the number expected to actually come.
Now Britain has announced that will extend to wider family members - adult parents, grandparents, children over 18 and siblings, alongside the groups already announced on Sunday.
There will also be a sponsorship route for firms to bring Ukrainians to the UK, who have no family already in Britain.
But No10 said there was no further extension for now, despite the EU preparing to announce all Ukrainian refugees can live and work for three years.
At least 400,000 Ukrainian refugees have entered the EU so far.
Boris Johnson told a press conference in Poland: “We will make it easier for Ukrainians already living in the UK to bring their relatives to our country.
"And though the numbers are hard to calculate, they could be more than 200,000”.
He added: “We’re 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’re 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 Prime Minister's official spokesman said that would widen eligibility to around 200,000 people, twice the number previously estimated.
Priti Patel confirmed the expansion of rules for Ukrainian family members to come to the UK.
The Home Secretary said for these people, the language requirements and salary thresholds that apply to most migrants will not apply.
But people who do not meet these requirements will only have permission to stay in the UK for 12 months.
And Ms Patel rejected pleas for a full visa waiver scheme - saying: “Russian troops are seeking to infiltrate and merge with Ukrainian forces. Extremists are on the ground in the region, too.”
She added: “Given this and also Putin’s willingness to do violence on British soil… we cannot suspend any security or biometric checks on people we welcome to our country. We have a collective duty to keep the British people safe and this approach is based on the strongest security advice.”
SNP MP Stuart C McDonald said: “Why is it that yet again at a time of humanitarian crisis, the Home Office is having to be dragged towards a generous and comprehensive response, instead of a shambolic and miserly mess?”
Ms Patel replied she found his comments "offensive and insulting".
The Home Secretary told MPs family members could apply at centres in Lviv, Poland, Moldova, Romania, and Hungary. A visa application centre in Poland is set to double capacity to 6,000 appointments per week, she said.
She added mum Valentyna Klymova, 69 - who tried to join her daughter but was turned away by UK Border Force at the Gare du Nord in Paris - is now in the UK.
Shadow home secretary Yvette Cooper voiced “relief” that Tory ministers had U-turned and done more - but added: “I have many questions about how this will actually work and how many people in people it will help.”
In response, Ms Patel admitted: “We do not know the numbers of people that will seek to come to the UK.”
Ms Cooper asked why there were no plans for a resettlement scheme like in Afghanistan. Ms Patel did not rule out a full resettlement scheme, saying: “This is a phased approach. We are looking at every single avenue.”
Labour also asked what would happen to stepchildren, to which Ms Patel replied: "It is a family scheme". Sources confirmed stepchildren will be eligible.
Ms Cooper also asked for a commitment that all family members will be welcomed “no matter what visa their family member here in the UK has”.
Lib Dem MP Alistair Carmichael said: “It is shameful that we are having to drag the Government inch by inch towards making a real commitment to the Ukrainians now fleeing Putin’s war machine.”
The UK Prime Minister arrived in Poland where he warned the Russian war in Ukraine "is worse than our predictions", "we’re seeing an unfolding disaster in our European continent."
Standing beside Poland’s Prime Minister Mateusz Morawiecki, he said: "Vladimir Putin is prepared to use barbaric and indiscriminate tactics against innocent civilians.
"To bomb tower blocks, to send missiles into tower blocks, to kill children, as we are seeing in increasing numbers".
Ukraine’s ambassador to the UK today warned Putin’s forces could try to starve Ukrainians.
Asked about the potential for a “food crisis” and looting, Vadym Prystaiko told the Commons Foreign Affairs Select Committee: “They will try to crush the will of the Ukrainian people to resist.
“We see problems with cash for example - people just running out of cash and they have interruption in their services.
“The terminals won’t be working and we will have to come up with some military solution to the distribution of food.”
He admitted Ukraine had to “pump up all the food we can until the routes are blocked”.
Lithuanian Foreign Minister Gabrielius Landsbergis warned it was clear Putin has "no boundaries" to what instruments he will use against Ukraine. “It is possible that this war will become a massacre," he told the UK’s Foreign Affairs Committee.
Earlier Boris Johnson warned “Putin will continue to tighten the vice”.
In Poland, Boris Johnson was meeting Prime Minister Morawiecki - before meeting NATO's Secretary General and UK troops in Estonia.
The Prime Minister was also due to meet Estonian Prime Minister Kaja Kallas and Estonian President Alar Karis this afternoon.
It comes after Oksana Markarova, Ukraine's ambassador to the US, said Russia had used a thermobaric weapon, known as a vacuum bomb, in its invasion of her country.
A vacuum bomb sucks in oxygen from the surrounding air to generate a high-temperature explosion that is capable of vaporising human bodies.
Concerns had been growing last night among Western officials that the weapons could be deployed.
They raised “significant concern” last night about evidence the TOS-1A thermobaric rocket launcher was present among Russian forces.
A Western official said: “Given the indiscriminate nature of that system, and it is certainly if it’s used in any form of built-up area, there is no way in which you could eradicate the risk of significant civilian casualties through the use of those sorts of systems.”
Boris Johnson said: “I’ve seen the reports about cluster bombs and thermobaric weapons - they will of course have to be verified, but I think everybody involved in the Russian onslaught should understand all this will be collated in evidence to be used at a future time in what could be proceedings before the International Criminal Court.
“If you’re going to use illegal weapons against innocent civilians, you’re going to be brought to the bar of history - or rather, to the International Criminal Court before then.”