Valid reasons include shopping, going to work, medical reasons and exercise once a day.
People are only allowed to meet up with one other person from outside their own household, and only when outdoors.
According to the rules, sitting on benches does not constitute exercise and may break rules around socialising.
When asked whether officers would question anyone sitting in the park during the lockdown, Priti Patel told BBC Radio 4's Today Programme: "Police have done that, let's be very clear about this.
"Throughout this coronavirus pandemic, during the last lockdown, the police have been asking individuals why are they out and about and should they be out and about, when the message right now is stay at home."
She added: 'We saw the number of cases of coronavirus yesterday - 62,000. Tragically over 1,000 people have died. That is one of the highest numbers since last April.
"We are in the thick of this shocking virus at the same time when we are trying to roll out a vaccination programme so it is right that we have these stringent measures and personally I think everyone has been incredibly responsible.
"Everyone has a responsibility to follow the rules and I think the British public will continue to do that."
The home secretary said more than 800 fines have been issued in the past two weeks for 'egregious' breaches of restrictions.
Officers have been told to issue fines more quickly to 'anyone committing obvious, wilful and serious breaches'.
Fixed penalty notices of £200 will be issued for a first offence. This will double for further offences up to a maximum of £6,400.
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