Deputy Chief Constable Jason Harwin said further measures were being considered about how to tackle the offender who was “completely ignoring the issue”.
“We’re looking at all our powers to see if there’s any options available to us,” he said.
These include work with councils and other partners on anti-social behaviour legislation such as closure orders.
Another two people had been issued three fines, while a fourth had been slapped with two penalties.
Under the new powers introduced by government, officers can hand anyone breaking lockdown rules a £60 fine – cut to £30 if paid within 14 days.
Second time offenders can get issued a £120 penalty, doubling further for each repeat offence.
Those who do not pay the fine can be taken to court where magistrates will be able to impose an unlimited fine.
However, Mr Harwin said the majority of people continued to comply with the regulations.
Police have now issued 151 fixed penalty notices – a rise on 19 since Wednesday.
Mr Harwin said the number of reports to police had declined, which he suggested was due to the weather over the past few days.