Staffordshire Police Chief Constable Gareth Morgan said crime levels and emergency calls were now back at usual levels, unlike at the height of the pandemic in April and May, meaning it would be more difficult for officers to respond to calls about people breaching the rules.
Meeting in groups of more than six is banned, while pubs will close from 10pm under tighter measures announced by Boris Johnson. Masks must also continue to be worn in shops and on public transport.
More Covid-19 coverage:
People have been encouraged to 'snitch' on their neighbours but Mr Morgan questioned forces' ability to deal with complaints. He said officers having to deal with breaches would mean "re-prioritising across the board".
The chief constable said challenges facing the police meant it was even more important that people follow the rules.
He said on Twitter: "The big difference at the moment is calls for service and crime are back to ‘normal’ so policing these latest regulations - and others that may follow - will mean re-prioritising across the board.
"That’s why we need everyone to do their best and follow the rules - for all our sakes."
People have been warned they face fines for not following the rules and the Prime Minister has said officers will be enforcing them, even suggesting the army could be called upon if needed.
Mr Johnson has said the latest restrictions - announced in a televised address to the nation on Tuesday night - could last up to six months.