After being pressed three times at a Downing Street briefing, the home secretary said: “The rules are clear, the rules are firm in terms of staying at home.
“The rules are tough enough.”
It comes amid speculation that Boris Johnson may tighten the restrictions in the coming days to get a firmer grip on the pandemic.
On Tuesday, official figures showed there were a further 45,533 Covid cases and 1,243 deaths within 28 days of testing positive for the virus.
The number of Covid-19 patients in hospitals in England stood at a record 32,202 as of 8am on Tuesday, according to the latest figures from NHS England.
Patel was leading the press conference alongside the head of the National Police Chiefs Council Martin Hewitt amid concerns that too many people are flouting the rules.
Hewitt said forces across the UK had issued almost 45,000 fixed penalty notices for “irresponsible behaviour”.
Examples of rule-breaking included a boat party in Hertfordshire with more than 40 people, a minibus full of people from different households travelling from Cheltenham into Wales for a walk, and someone hosting a party but claiming it was a business event.
Patel said the “horrifying” death toll underlined the need for people to follow the rules, blaming “a minority of people” for “putting the health of the nation at risk by not following the rules”.
She repeatedly insisted that the rules are “clear”, despite questions over what constitutes local exercise after the prime minister travelled seven miles from No.10 to cycle around the Olympic park.
Outdoor recreation was permitted “in a very, very restricted and limited way, staying local”, Patel said.
Hewitt meanwhile dismissed the calls from senior police officers, including the Metropolitan Police commissioner Cressida Dick, to make the rules around what constitutes “local” exercise more clear.
“If you tried to make a definition for every possible circumstance that would be really challenging,” he said.
“I don’t think we are in a position where we want to set a particular distance because how would – if a police officer stopped somebody – prove that a person is within or outside that distance.”
Despite insisting the rules are tough enough, Patel said the government would keep the restrictions in England under “constant review”.
“In government, there are endless discussions taking place about the state of coronavirus, support and capacity within the NHS, and also lockdown measures right now,” she said.
“We are not going to speculate on anything. These issues are live within government.”