Boris Johnson told the House of Commons on Wednesday a thousand visas had been granted under the Ukraine Family Scheme allowing relatives of people in Britain to flee the war zone to join their families.
The Prime Minister also promised another programme allowing individuals to offer a home to Ukrainians would be set out in “the next few days”.
He said: “We know how unscrupulous Putin can be in his methods, it would not be right to expose this country to unnecessary security risk and we will not do it.
“We are going to be as generous as we can possibly be, but we must have checks.”
However the UK has come under fire after it emerged only 300 visas to Ukrainian refugees have been granted after 17,700 applications.
The BBC reported from Britain’s visa application centre at Rzeszów in Poland, where Antonina Kolodii, 79-year-old refugee and professor, warned there could be riots.
She said: “It’s really quite desperate. There is no system in place, it’s quite clear that this place is understaffed, quite severely, that there is absolutely no way that people who work here can process so many applications.
“So it’s not working. People are very frustrated, very angry. They ran out of patience.
“If this continues for much longer, it does feel like there will be riots.”
READ MORE: Ukraine LIVE: Putin on alert as UK and NATO poised to deploy 5k-strong
Marianne Kay, 43, daughter of a Ukrainian refugee also called the UK visa system an “absolute mess” after members of the police were called to calm “angry” crowds at Rzeszów.
Ukrainians fleeing the invasion could be seen banging on the glass of the application centre’s windows in frustration, after being told by the centre’s staff they were only able to see 100 applications per day.
Ms Kay, who works in IT management at the University of Leeds, said of the scene: “People were angry, they lost patience – they are very tired.
“It was obvious (the staff) were scared of the crowds because it is scary.
“Eventually the police came because it was so loud and so bad … people were on the street banging on the windows because they wanted to come in.”
According to The Herald, Ms Kay flew to meet her 79-year-old mother, who made the journey from Lviv and through the Polish border to Rzeszow, in order to help her submit biometric data for her Ukraine Family Scheme visa application.
She and her mother, a professor of political science, drove two and a half hours to the centre from Krakow on Monday.
The doors were shut later in the afternoon when the centre hit its 100-person capacity.
They returned on Tuesday, where staff informed the crowds that they would not work through a list created the previous day, but instead will “prioritise people who booked appointments through the website”.
Ms Kay then said: “The whole process was designed to let as few Ukrainians in (to the UK) as possible.
“It’s confusing as hell and the rules are changing every day – it’s impossible to complete the process.
“It is the hardest, most dehumanising and humiliating process in comparison to other countries.”
It comes as Tory MPs shared their anger over Home Secretary Priti Patel’s evacuee programme, after it emerged only Ukrainians with permanent UK residency rights can be reunited with relatives fleeing the war.
The Home Secretary also faced calls to resign for telling MPs on Monday a visa centre had been set up near Calais.
In fact, it is not due to be operational until later on Wednesday in Lille, around 70 miles away.
Sir Roger Gale, Tory MP for North Thanet, told the Commons: “That was untrue and under any normal administration that in itself would be a resignation issue.”
MP Alec Shelbrooke told Mr Foster: “We want dates, we want action and the Home Office must react far more quickly than it’s doing, and get to the point of hubs of people, get them processed and get them in. This is a disgrace.”
Former immigration minister Mark Harper said the Government needed to “grip the pace of this”.