Some 1,200 people have been questioned by West Yorkshire Police under the new legislation, brought about to help UK police to enable social distancing in public spaces.
The force's Chief Constable John Robins told the Home Affairs Select Committee today (Monday) that since the lockdown powers came into force, his officers had also issued 20 fines.
North Yorkshire Police meanwhile has issued 11 fines since Thursday.
It comes after a weekend where the public were urged not sunbathe despite a recent spell of pleasant weather.
Sunbathing is banned under coronavirus-tackling measures, Downing Street said, but it is up to police to use "discretion" in enforcing the rules.
The Prime Minister's official spokesman said: "We did set out very clearly the reasons why people should leave their houses and sunbathing was not one of them. People shouldn't be going to beaches or parks to sunbathe, it goes against our guidelines on essential movements.
"We gave the police powers to implement those guidelines and it's up to them to exercise discretion over how they do so."
Simon Kempton, from the Police Federation, also told today's Home Affairs Select Committee that a minority of people still do not want to comply with the measures set out by the Government.
"The vast majority of the public get it, they understand why this is so important and it's inconvenient and would rather it wasn't the case, but they get it and they want to comply, they want to help, they want to do their bit.
"But there are still a minority of members of the public who simply do not wish to comply with the restrictions.
"And we saw over the weekend with the nice weather, some of my colleagues having a monumental task, one or two officers to empty a park with hundreds of people in it.
"And most of those individuals wanted to argue their case as to why they were doing something within the guidelines.
"What would help perhaps is engaging the public on an emotional level so more of them wanted to comply, not just that they felt they had to comply, but they wanted to comply."