Two police and crime commissioners have called for fines to be increased in Wales for those breaching lockdown rules.
Fines in Wales currently begin at £60, and rise to £120 if people have already received a fixed penalty notice under the same regulations.
However, fines in England now start at £100 and can reach up to £3,200 for repeat offenders.
The Welsh Government has said it is not planning to change the fine system, but will keep it "under consideration".
Gwent Police's Chief Constable Pam Kelly would not be drawn on whether she thought fines should be increased in Wales. She told ITV Cymru Wales there would not be "border policing".
"We are making sure that Welsh law is applied in Wales", Ms Kelly said, "so we are working with friends and colleagues working across the border to make sure that people know that if they are travelling into Wales, Welsh law applies.
"We have visible policing, not border policing, but visible policing, communicating with people to make sure that they understand that the law applies here.
"This is a behaviour issue, people need to think about their behaviour and the impact that their behaviour is having on other people's lives".
Pam Kelly said her force had also recovered 347 vehicles in Gwent that were either not insured or there were sufficient evidence of criminal activity.
On Thursday, two police and crime commissioners (PCCs) called on First Minister Mark Drakeford to increase the fines.
The commissioners and chief constables for all four police forces in Wales will be writing to the Welsh Government over the issue, the two said.
They also urged Mr Drakeford to award police in Wales the powers to evict those staying in second homes.
Arfon Jones, Plaid Cymru PCC for north Wales, said the movement of people from more densely-populated areas with higher infection rates to more rural communities was creating "tensions".
"The local population is understandably anxious about the prospect of rising infection rates, which is already predicted by the health board due to a later peak than in the more densely populated south of Wales," Mr Jones said.
"Our priority is to protect these communities."
In Wales, lockdown regulations state that people must exercise locally.
Dafydd Llywelyn, Plaid Cymru PCC for Dyfed-Powys, said the easing of travel restrictions in England meant Wales needed to be stricter with fines.
"We need greater powers to act as a deterrent or to enforce that people do not use second homes," he said.
"Lockdown measures here are stricter but with lower fines.
"The penalty in Wales doesn't fit the crime and isn't working - we had one repeat offender in Llanelli who offended five times and yet the maximum fine will be #120.
"It feels as though the first minister has given us a spoon to cut down a tree."
In a statement, a spokesman for the Welsh Government said: "We are not planning to change the fine system in Wales at the moment, but we are keeping the matter under consideration."