Mr Oliver criticised the SNP over its handling of the coronavirus pandemic in Scotland. The TV presenter also raised concerns over the fairness of the upcoming Holyrood election.
Writing in The Sunday Times, Mr Oliver said the SNP’s approach to the pandemic “is the latest and most troubling provocation for those moved only to shudder and look away.”
He said the SNP has made him “sick to my stomach”.
Mr Oliver added: “Every day Sturgeon stands at her podium and performs her greatest hits — about how hard she and her team are working, how much she cares, that she won’t be answering that question now — and there is an audience somewhere holding aloft its lighters and singing along.
“For the rest of the population it is a shaming spectacle. For many Scots the SNP has made a fool of Scotland.”
Mr Oliver claimed that allowing the First Minister to present daily coronavirus briefings, while at the same time halting election campaigning due to the pandemic, is a threat to the fairness of the election in May.
He wrote: “Any independent team travelling the world to monitor the safety, legality and fairness of elections would surely witness such an egregious imbalance and be on the first plane out of the country to raise the alarm.
“In Scotland hardly a soul is moved to bat so much as an eyelid.
“Much more of this and Scotland will be the sort of place the Foreign Office tells travellers to steer clear of. Is that the tinpot clang of a dictatorship?”
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She said: “At a time like this, I’m not going to stop doing my job because it is really important as we steer the country through this pandemic.”
The First Minister added: “I am not going to stop doing my job for as long as I’m in this job that I’m doing.
“How people report that and how people take account of the election campaign, I’m sure will become clearer as we go on. We’re not there yet.
“We’re in this pandemic, we’re undertaking a massive logistical exercise with the vaccination programme – that will continue to be what I focus on.”
Liberal Democrat MP Alistair Carmichael previously called for health professionals to take over the role at the coronavirus briefings during the campaign.
He said: “I am sure the First Minister would not want to use sober and serious press briefings for her own narrow advantage during an election campaign.
“There are able communicators like the national clinical director, chief nursing officer and the chief medical officer who could take on the heavy responsibility of the daily briefing for the period of the election. That would be the sensible way to proceed.
“In April and May if the virus is so out of control that the First Minister judges she must do the daily briefing herself it does beg the question as to whether you can have a valid and safe election.”
Recess at Holyrood is expected to start on March 25 – six weeks ahead of the election in May.
The BBC has been approached for comment.
In December, the BBC told Express.co.uk: “We’ve had on-going discussions with Lord Foulkes about our coverage of the briefings. At this point in the pandemic audiences are demonstrating a significant interest in accessing relevant public health information in this way. Similar briefings are broadcast by the BBC elsewhere across the UK.”