He told MPs: “There is a plane ready and waiting in Poland to bring these orphans to the UK on Friday but that flight will leave empty without the necessary paperwork from the Home Office.
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“The Polish authorities, Edinburgh City Council, the Scottish Government and the orphans’ guardians are all working to bring these children to safety.”
Mr Blackford thanked refugees minister Lord Harrington for his efforts, then added: “But a week on, the Home Office is still proving to be the only obstacle in the way and it risks leaving these children stranded.
“So I’m pleading with the Deputy Prime Minister: remove these obstructions before it’s too late.”
However, Dominic Raab, who was standing in for Boris Johnson, claimed the Home Office was not at fault.
He said: “We want to do everything we can.
“Of course there are range of issues in this case, including the wishes of the Ukrainian government on where orphaned children should go and should be living, whether any necessary permissions are being sought from the Ukrainian and/or Polish governments.
“This isn’t actually about bureaucracy, it’s about genuine safeguarding issues but I certainly want to work with him in the best interests of those children.”
Mr Blackford said the Polish and Ukrainian authorities have offered their support, adding: “We need the Home Office to give us the paperwork that’ll make that happen.”
Mr Raab replied: “It’s very important that the proper international practices on safeguarding are followed, I know he appreciates that.
“We’re keen to find out if family reunion options with Ukrainian family in the region have been considered, we also know that many children in state care in Ukraine have family members in the region – for the safeguarding and wellbeing of the children that must also be considered.”
Duncan MacRae, the media manager for Dnipro Kids, who is currently over in Poland helping the children said: “We really appreciate the support that certain politicians have been giving us. They’ve been very keen to put pressure on the UK Government”.
He believes that Raab’s safeguarding concerns shouldn’t apply to the children being helped by Dnipro Kids. He said: “The orphans we support all have their carers with them – what we would call their orphanage mums.
"They are the children's guardians and as we have accommodation ready and waiting to keep the children and their guardians together, the excuse of safeguarding doesn't appear to be applicable to these orphans' situation.”
The charity has successfully sourced accommodation that will enable it to keep the members of each orphanage - around seven to 12 people - together.
Mr MacRae has called on the Home Office to contact the charity directly, and said: “They simply need to make the choice to let these children in. We would be happy to talk and get this done.”
The orphans are currently staying near Poznan, in Poland, in a hotel – the top floor of which has been reserved for Ukrainian refugees.
When they arrived, they were told they could stay for 14 days, which will be up at the end of this week.
While Mr MacRae believes the hotel will allow the children and their guardians to stay until they get the green light to travel to Scotland, he said: "It's extremely frustrating, and it's heartbreaking to know we can't give these children the clarity they need about their future.
“They've already been through a lot of tough times in their short lives.
“The last few weeks have been a terrible ordeal for them to deal with.
“We just want to keep them safe and get them settled somewhere as soon as possible.”
Dnipro Kids was set up in 2005 by Hibs fans, following a UEFA Cup trip to the Ukrainian city of Dnipro.