The National Police Chiefs' Council confirmed fixed penalty notices had been handed out, but have yet to release details of how many and in which areas.
Those who ignore restrictions on movement can now be fined £60, with the fine doubling after each offence.
Police can also take steps to make sure parents are stopping their children from breaking the rules.
According to the guidance issued by the Home Office, the cost of initial fixed penalty notices will be cut to £30 if paid within 14 days - but those who do not pay could be taken to court and risk facing costs for unlimited fines.
Meanwhile, Cumbria Police has warned members of the public looking to visit the area they risk getting fined, announcing: "The Lake District is closed".
The force urged people to show "common sense" and not travel into the region, adding those who do can expect to be stopped and asked if their journey is essential.
The force's temporary Chief Superintendent Rob O'Connor said: "We do not want to see people travelling to the Lakes in caravans and camper vans, or driving many miles in their cars to go walking on the fells.
"The Government guidance is really clear in relation to personal movements to limit the spread of coronavirus."
He added: "It does not mean on nice days you can drive into the Lakes and go walking, or ride your motorbike to Devil’s Bridge at Kirkby Lonsdale."
Mr O'Connor said he would rather officers not have to "resort to" issuing fines, but reminded the public of the powers to now do so.
Elsewhere, Derbyshire Police has defended using drones to deter people from flouting lockdown rules by walking in the Peak District.
The force filmed people rambling in the beauty spot on Wednesday, saying travelling to remote areas for exercise did not count as "essential travel".
Meanwhile, officers from Avon and Somerset Police have been conducting random vehicle checks in Bristol to ensure only essential journeys are being made.