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"I would have thought that for most people, a walk of up to an hour, or a run of 30 minutes or a cycle ride of between that, depending on their level of fitness is appropriate."
Mr Gove said most people were already displaying "common sense" when it came to following social distancing guidelines.
But he warned that tighter curbs could be brought into force if people fail to follow the Government's orders.
Repeated statements from the government that if people continue to stretch the rules, they will be tightened, a statement from the Royal Parks and a conversation with an officer in the Royal Parks Police.