David Carter, a transport manager from Driffield, fled from eastern Ukraine last month along with his wife Maryna and her children Sasha, 15, and Zlata, six.
The family drove hundreds of miles and witnessed scenes so horrific that Zlata fainted on crossing the border into Poland.
After crossing the border, the family journeyed to Belgium where Mrs Carter and her children applied for a visa last Tuesday March 1 under the refugee visa scheme announced by Priti Patel.
But despite being told there would be a 48 hour turnaround, the family have been forced to spend over £1000 on a hotel in Calais while waiting for the visas to be approved.
The family tried to cross the Channel on a ferry, but were turned away at the dock, Mr Carter told the Yorkshire Post, leaving the children in tears.
He said: “I’ve was in the east of Ukraine when the bombing started.
“I just got in the car and set off. There were armoured vehicles being blown up, and Ukrainian soldiers on the floor. I told the kids to close their eyes.
“In the early hours of the morning at the Moldovan border they opened fire, and I spun the car around.
“I looked at the maps and thought ‘I need to head to Lviv.’
“Nobody can understand how awful it’s been, I’ve never seen so much devastation in all my given days.
“Zlata fainted. Her lips were blue, I was crying my eyes out. What could I do? We’ve just hoped for the best.”
Mr Carter’s daughter, Jordan-Chelsea, was tracking the family’s progress on the Find My iPhone app, and helped her father source a visa office in Brussels, which he visited on March 1.
Mrs Carter and the children had their biometrics taken and submitted evidence including birth certificates and letters from their biological father authorising their leaving Ukraine.
They then journeyed to Calais to travel on the first available ferry when their visas were approved.
But almost a week later, no visas have been issued, with the Home Office saying it was missing evidence the family insist has been submitted.
Mr Carter said: “I’m not being big-headed but I don’t need anything from my government. I don’t need any money from them, and I can adequately adapt my house and my family, including in-laws.
“But it’s now about how they look at our visas. It’s a terrible situation.
“I’ve done everything correctly. I don’t know what the problem is. This is costing me money, but it’s not about the money. It’s about us getting home.”
Mr Carter hopes to be able to house his in-laws, who are still in Ukraine, if he can help them get across safely once he reaches the UK.
Jordan-Chelsea Carter, 24, said: “We’re absolutely deflated. The government are saying one thing to the nation watching the news, but for the people suffering it’s a different story.
“It’s not like my Dad can just ring up Boris Johnson. There’s nothing we can do.
“We’ve sent the documents and we’ve heard nothing since. It’s like waiting for Christmas.”
The Home Office has been approached for comment.
It comes after theHome Office revealed that only "around 50" visas had been granted under the Ukraine Family Scheme as of 10am on Sunday but Boris Johnson said that "thousands" of applications were being processed.
As well as the visas on offer to those with family in the UK, a humanitarian sponsorship scheme will allow people and organisations to bring Ukrainians to the UK.
The Prime Minister said: "As the situation in Ukraine deteriorates, people are going to want to see this country open our arms to people fleeing persecution, fleeing a war zone.
"I think people who have spare rooms, who want to receive people coming from Ukraine, will want us to have a system that enables them to do that. And that is already happening."