Figures published by the Office for National Statistics for England and Wales brought the United Kingdom's official death toll to 38,289 as of May 3, according to a Reuters tally of death registrations that also includes Scotland and Northern Ireland.
First Minister Nicola Sturgeon has kept all existing lockdown measures for at least another three weeks, but eased "one small aspect" as she allowed socially distanced walking and exercising outdoors a couple of times per day.
The government is expected to set out more details on the measures on Monday.
The source said: 'I think what's actually happened is that the Leader of the Opposition has inaccurately and selectively quoted from the Public Health England guidance and that is what the PM was referring to'. "If you can work from home, go to work".
He said: "First and foremost, everyone should recognise that in Scotland the advice remains the same this week as it was last week, and that is for everybody to stay at home, to protect the NHS, with the intent of saving lives".
But with ministers encouraging employees to return to work where possible, he urged people not to "flood back" on to public transport, warning that the system will not be able to cope.
Labour's shadow home secretary Nick Thomas-Symonds told BBC Radio 4 the speech left millions of workers in an "uncertain position" over whether to go to work if they felt unsafe on Monday.
He also announced plans to introduce a 14-day quarantine for people arriving in Britain by air to prevent new infections from overseas.
"Or the fact they claimed comparisons with other countries is unhelpful and started claiming that after seven weeks of publishing comparisons with other countries every day and only started complaining they were unhelpful when we became the worst hit country in Europe".
Because of this, new lockdown rules state that "as well as exercise, people can now also spend time outdoors subject to: not meeting up with any more than one person from outside your household; [and] continued compliance with social distancing guidelines to remain two metres (6ft) away from people outside your household".
He said parts of the hospitality sector "and other public places" could be cleared to reopen at the earliest in July.
The government has also said that people will now be allowed to drive as far as they want in England to go to an outside space.
The next steps of lockdown easing - including the phased return of schools for all pupils, reopening of non-essential retail, and permitting of cultural and sporting events - will depend on up-to-date assessments of risk, the plan says.
"And in turn that Covid alert level will tell us how tough we have to be in our social-distancing measures - the lower the level, the fewer the measures".