ITV News International Affairs Editor Rageh Omaar, who is travelling with the prime minister, reports on Boris Johnson coming face-to-face with Ukrainian frustration at what its people feel is a lack of Western action.
The prime minister said he could not implement a no-fly-zone because it would see the UK and Nato "shooting down Russian planes" - a move experts say would spark a reaction from Vladimir Putin that would lead to World War III.
Daria Kaleniuk, who is from Kyiv but crossed the border to Poland, told Mr Johnson of the "deep fear" Ukrainian women and children feel because "bombs and missiles which are going from the sky".
"You’re coming to Poland, you're not coming to Kyiv," she said, "because you are afraid, because Nato is not willing to defend, because Nato is afraid of World War III, but it has already started."
Ms Kaleniuk, the executive director of the Anti-Corruption Action Centre civil society organisation, added: "Ukrainian people are desperately asking for the rights to protect our sky, we are asking for a no-fly zone - what's the alternative for the no-fly zone?"
Mr Johnson said: "I'm acutely conscious that there is not enough that we can do, as the UK government, to help in the way that you want and I've got to be honest about that.
"When you talk about the no-fly zone, as I said to (Ukrainian President) Volodymyr Zelensky a couple of times, unfortunately the implication of that is the UK would be engaged in shooting down Russian planes, it would be engaged in direct combat with Russia.
"That's not something that we can do or that we've envisaged. The consequences of that would be truly very, very difficult to control."
The PM told Ms Kaleniuk he believes his economic sanctions are working, that Putin's invasion of Ukraine "is doomed to fail" and it will be "extremely difficult for him to continue on the path that he is on".
But the reporter attacked the UK sanctions, saying Chelsea FC owner Roman Abramovich "is not sanctioned, he's in London, his children are not in the bombardments, his children are there in London".
Speaking after she made her emotional plea to enforce a no-fly zone, Ms Kaleniuk told reporters that without a no-fly-zone, "Ukrainian children, Ukrainian hospitals will be hit with missiles and bombs".
She attacked Mr Johnson's reluctance to enforce a no-fly-zone, saying Britain had guaranteed the security of Ukraine after the fall of the Soviet Union, "and now Britain's prime minister comes to Poland and says 'no way we can't hit Russian planes'".
She added: "It is Ukrainian babies and children who are now guaranteeing security for the West, because the West is afraid."
Ms Kaleniuk said Ukraine's Western allies "knew everything would happen, they knew that there would be a devastating war but no one is prepared for that".
'Without a no-fly-zone Ukrainian babies and Ukrainian hospitals will be hit by bombs': Daria Kaleniuk on why she wants a no-fly-zone
The PM ruled out any involvement in the conflict but told his Polish counterpart Mateusz Morawiecki at the press conference that "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".
Asked about Ms Kaleniuk no-fly-zone request during a later visit to Estonia, Mr Johnson said it's "important to understand Nato is a defensive alliance".
"This is a time when miscalculation and misunderstanding is all too possible and it's therefore crucial that we get that message over.
"When it comes to a no-fly zone in the skies above Ukraine we have to accept the reality that that involves shooting down Russian planes ... that's a very, very big step, it's simply not on the agenda of any Nato country."
At least 400,000 Ukrainian refugees have entered the EU so far, according EU Home Affairs Commissioner Ylva Johansson, and the UK has been criticised for not waiving visa rules for all Ukrainians fleeing the invasion.
Home Secretary Priti Patel relaxed some immigration rules on Monday to allow Ukrainians with immediate family in the UK to "seek sanctuary" there, a move she said would allow an extra 100,000 to enter the UK.
The EU on the other hand announced on Sunday it would accept an unlimited amount of Ukrainians fleeing war, without asking them to apply for asylum first, allowing them to remain for up to three years.
The nations of the European Union have been told to "prepare for millions" of refugees in the coming weeks and months.
But Ms Patel said the UK would be unable to do the same after receiving the "strongest security advice".
"We know all too well what Putin's Russia is willing to do, even on our soil, as we saw through the Salisbury attack and through the nerve agent use on the streets of the Ukraine."
Why has Russia invaded Ukraine and can Putin be stopped?