However, before the plane left Heathrow Airport, a form that should have been sent by the Ukrainian government to the Polish Ministry of Family and Social Policy, needed to release the group, was not sent in time.
It is now said that the Virgin flight will not take place before Wednesday, with organisers looking at alternative options.
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The children and their carers are now awaiting the next flight in a hotel.
It came after Home Secretary Priti Patel announced on Thursday that the youngsters, who are being cared for by the Scottish charity Dnipro Kids, which was set up by supporters of Edinburgh’s Hibernian Football Club, had been given the green light to travel to Britain.
SNP Westminster leader Ian Blackford, who was due to join the flight, told the PA news agency: “We’ve been up against a race against time to get the paperwork that needs to be in place signed off on and there’s been a delay on that.
“So, for the time being, it means that nothing is going to happen today.
“I think the key thing is that a lot of people will determine everything is done to support the orphans that are currently in Poland.
“That has always been the first and last concern of all of this, so we’ll continue to work with everybody to make sure that arrangements can be put in place to give the children that sanctuary in Scotland.”
Dnipro Kids was set up in 2005 after football fans visited local orphanages when Hibernian played against the Ukrainian team Dnipro FC.
The youngsters were due to spend Tuesday sightseeing in London, before heading to rural Stirlingshire on Wednesday.
A Home Office spokesperson said: “It is deeply troubling that these children have been caught up in (Vladimir) Putin’s brutal invasion of Ukraine.
“It is right that we only move these children once we have the full, written agreement of their home and host governments.
“The Home Secretary and her counterparts in the Ukrainian, Polish and Scottish Government are united in their determination to ensure these children get the support and care they need.”
A statement from Project Light, the operation to transport the children to the UK, said: “The group, made up of 52 children and seven adults, are currently being taken care of at a hotel in Poland and are safe and well.
“The final paperwork required by the Polish Ministry of Families did not arrive in time for the flight to leave today.
“All the parties involved in this mission are working hard to bring them to the UK in the coming days.”