She claimed Home Secretary Priti Patel was “repeating the same mistakes we've seen the UK Government make throughout this crisis” by failing to restrict international travel or introduce a rigorous system of health checks and quarantining.
The Edinburgh MP also said the Home Office must bring the UK “into line with other countries” where tighter measures are being placed on travel.
Her comments came just hours after First Minister Nicola Sturgeon said international travel was “effectively banned” in the new lockdown.
At her daily press briefing, Ms Sturgeon said: “You should not be going overseas unless it is essential and you should not be coming into Scotland unless it is essential. That's different to actual physical control of the border, but that's the legal position. We have effectively said travel is banned and that is a message that I want to get across very seriously.”
She also said she had discussed the prospect of new border controls with UK leaders.
“I had a four-nations discussion last night, chaired by Michael Gove from the UK Government, where the issue of borders, stricter restrictions on travel and controls at the border was discussed," she said. “There was an agreement in that call to take forward some urgent four-nations discussions about that over the course of the days.”
Despite the commitment to talks on border controls, Ms Cherry urged the UK Government to take urgent action immediately.
“It is deeply concerning that the Home Secretary is repeating the same mistakes we've seen the UK Government make throughout this crisis by failing to introduce effective restrictions and health measures at the UK border to prevent the transmission of Covid-19 and its new strains,” she said.
“The UK Government was far too slow to act in the spring, allowing hundreds of thousands of international visitors to enter the country in the middle of a global pandemic without effective measures in place. It seems as though they haven't learnt a thing.
“No-one wants to restrict international travel, but it is a necessary part of mitigating against transmission. The UK Government must stop all but essential travel and introduce a far more rigorous system of health checks and quarantining at the border. This is a matter of urgency and the Home Secretary must get a grip of the situation.”
She added: “When the SNP called for these measures during the first wave of the pandemic, the UK Government dismissed our calls for many weeks before finally U-turning and introducing an ineffective system for too short a period.
“Other countries in Europe and across the world have already introduced these measures – leaving the UK as an outlier. For people to have confidence in the UK Government's approach, it is crucial they put these long-overdue measures in place.”
Earlier today Mr Gove said the UK Government would be “coming forward very shortly with new proposals on how exactly we will make sure that our borders are safe”. “But the message is very, very clear for UK citizens that they should not be travelling,” he said.