A government adviser has accused ministers of confusing people by urging them to “stay at home” while also quietly allowing more staff back to their workplaces.

Aides to Priti Patel, the home secretary, have issued a stinging warning that police could be given beefed-up powers to enforce lockdown measures, claiming a “small minority” are flouting the travel ban.

But Susan Michie, a health psychologist who sits on the advisory Sage committee, said ministers were creating “a real problem” with their “mixed messages”.

In recent days, the government has sanctioned a growing numbers of businesses, including DIY stores, construction firms and takeaway food chains, to reopen – requiring their workers to travel, she said.

“What we have seen this last week is that many employers are opening up business again,” said the professor at University College London.

“We must realise that some people are responding to what they are being asked to do, they are not flouting the rules.

“It is very, very difficult when we are getting mixed messages from the government – on the one hand stay at home, on the other hand go into non-essential work.”

Ms Michie said people had “a powerful influence” on each other, telling Sky News: “It may be that people then think, ‘well they are out and about, I think I will go out and about too’. We have a real problem there.”

The comments are significant because the professor is a member of the Covid-19 behavioural science advisory group as well as Sage, the scientific advisory group for emergencies.

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They come as a debate rages in the government and the Conservative Party about when and how to relax restrictions, ahead of Boris Johnson’s expected to return to work on Monday.

Traffic levels on the roads have begun creeping up this week and there have been scenes of sizeable crowds in shopping centres and parks in recent days.

Motor vehicle use was recorded at 38 per cent of pre-lockdown levels during the first three days of last week – but rose to 41 per cent from Monday to Wednesday this week.

But the criticism was rejected by Ms Patel, at the daily Downing Street press conference, who said: “The government message has been clear and consistent from day one about staying at home.

“We have also been clear that, if you can’t work from home, you can go to work. There are no mixed messages. We have been clear, the police have been clear.”

The clash came as the home secretary played down hopes of an early easing of the lockdown as the death toll in hospitals passed 20,000.

She called it a “deeply tragic and moving moment”, warning “we are not out of the woods yet” – and telling people to stick to social distancing instructions.

“The government has been abundantly clear about the five specific things that have to be satisfied – this is not optional – so that we can consider with the scientific advisers when it will be safe to adjust the current measures.