The Covid rate for Scotland was record in the week to July 10, according to new figures from the Office for National Statistics (ONS).
This is an increase on the previous week, when the figure was one in 100, and the highest level since the ONS infection survey began in October.
The rate in England was one in 95 people.
It comes as the daily case rate for the UK climbed above 50,000 for the first time in six moths.
Professor James Naismith, director of the Rosalind Franklin Institute at the University of Oxford, said cases would likely continue to rise across the UK.
It comes ahead of restrictions easing on Monday, when all of mainland Scotland will move to level zero and almost all restrictions will be removed in England.
Renewed calls have been made for the Covid vaccination programme in Scotland to be sped up, as it becomes increasingly likely that not all adults in Scotland will receive a first dose by July 18 in line with the Scottish Government target.
The calls came as fresh data showed more than 20 per cent of all calls to the national vaccine helpline were abandoned in May, rising to 32 per cent for the past two weeks of the month.
On May 24, June 5 and June 7, over half of all calls were abandoned.
On May 24, those calling to register for a vaccine faced an average wait of more than 23 minutes.
Scottish Labour said the figures raised concerns about whether the helpline had the resources it needed.
Deputy leader and health spokesperson Jackie Baillie said: “It is deeply worrying that thousands of Scots who are seeking help or guidance on the vaccine programme are being left hanging on the telephone or having to give up without answers.
“We simply cannot have thousands going without the help and guidance that they need.
“It is the duty of the Scottish Government to ensure that the vaccine helpline is fit for purpose and that staff are properly supported in carrying out their duties.”
A total of 51,870 Covid cases were reported across the UK on July 16 – the highest figure since January 15, when 55,761 cases were reported.
Prime Minister Boris Johnson earlier this month warned the number of new cases could reach 50,000 a day by July 19.
The latest daily case total is still some way below the peak of the second wave of the virus, which saw a high of 68,053 cases reported on January 8.
But the numbers are on a clear upwards trend, with average daily cases up 35 per cent week-on-week.
UK health secretary Sajid Javid has said the number could top 100,000 over the summer.
Some 2,047 new cases were reported in Scotland on Friday.
A total of 532 people were in hospital with recently confirmed Covid-19, down 11 in 24 hours, with 48 of these patients in intensive care, up one.
Five new deaths within 28 days of a positive test were recorded – a drop on Thursday’s figure of 19, the highest daily number since March 11.
Professor Naismith said it was a “reasonable assumption” that cases would continue to rise.
While the numbers of cases reported daily appeared to plateau across the UK last week, he said this was likely not to reflect the true picture, and the ONS measure was the “gold standard”.
He said: "Today’s ONS data show that in Scotland and England more than one person in every 100 has Covid-19. Wales and Northern Ireland have less, around four in 1,000.
“These data show that up to last Saturday, the Delta wave has continued to grow, as expected. This is the last ONS update we will get before the quasi end of restrictions on Monday.
"It is a reasonable assumption that the wave has continued to grow this week and will accelerate after Monday. We are doubling cases every 12 to 18 days.”
He added: “New cases of Delta will lead to long Covid, hospital admissions and deaths.
“The ratios between these have been massively changed by the safe and effective vaccines we are administering, but the link is not eliminated.”
All of mainland Scotland will move to Level zero on Monday.
Up to eight people from up to four households will be able to meet within homes, while outside up to 15 people from 15 households will be able to gather either in private gardens or public places.
Up to 200 people will be able to attend weddings and funerals, but under new changes made by the Scottish Government in response to high numbers of Covid cases in recent weeks, hospitality venues will have to shut at midnight.
Opposition parties have called for the vaccination programme to be further sped up in light of the high cases.
Scottish Labour renewed calls for the gap between vaccine doses to be cut to six weeks, following the example of Northern Ireland.
Ms Baillie said: “This proves that we can speed up vaccination when needed – the SNP are simply choosing not to act.
“The evidence is piling up by the day on how effective double vaccination is against the Delta variant, but we are still dragging our feet – and against the recommendations of the WHO at that.
“The science is there and so are the vaccine stocks – all that is missing is the political will.”
Nicola Sturgeon has called previous demands from Labour to cut the dose gap “irresponsible” and not in line with JCVI guidance.
A spokesperson said the Scottish Government would follow JCVI advice.
“We note comments from JCVI adviser Professor Anthony Harnden, who underlines that real data vaccine effectiveness studies show a lower vaccine efficacy with shorter intervals and that modelling suggests the number of infections could actually rise,” the spokesperson said.
Scottish Conservative shadow health secretary Annie Wells labelled plans to close the SSE Hydro in Glasgow as a vaccination centre ahead of COP26 “confusing”.
She said: “Just as we head towards the finishing line, the SNP are overseeing a slowing down in Scotland’s vaccination rollout.
“They are set to miss their own targets and hundreds of thousands of adults are still set to be waiting on getting their first dose.
“People will understandably be confused as to why the decision has been taken to close the country’s largest vaccination centre.”
Health secretary Humza Yousaf said the move would have “no negative impact” on the vaccination programme.
He said mass vaccination centres had seen more no-shows to appointments than smaller centres.