Businesses including pubs, cinemas, theatres and casinos were told to close from 21 March, as part of government drive to reduce the spread of coronavirus.
Sussex Police said it had received calls from people concerned that some such businesses were still open – but said that this was ‘not a policing matter’.
It urged people to keep its lines free for people who need police assistance.
A spokesman said on Twitter: “We’ve had calls about premises still open following yesterday’s Government statement.
“Not policing matter but we expect businesses want to support the measures.
“Some cafes and restaurants operate a takeaway service not affected.
“Please keep our lines free for those who need us.”
On Sunday, the Government issued guidance on how the regulations would be enforced, confirming that it would be the responsibility of local government to ensure businesses complied with the request to close.
Businesses which do not follow the COVID-19 restrictions will be issued with prohibition notices, a spokesman said.
They will receive fines and could also face the loss of their alcohol license.
Environmental Health and Trading Standards officers will monitor compliance and issue the prohibition notices if necessary, the spokesman said.
Under the Business Closure regulations introduced on March 21, officers will have powers to prosecute for breach of regulations.
Robert Jenrick MP, Local Government Secretary, said: “We recognise the pressure the emergency COVID-19 restrictions place on small businesses, which is why the government has announced an unprecedented package of support to help businesses and workers.
“But we must follow the medical advice.
“That means staying at home, protecting the NHS and saving lives.
“So far we have seen this crisis bring out the best in us, but some people are risking the safety of others by failing to act on medical advice.
“People must do this immediately to save people’s lives.”
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