Welsh First Minister Mark Drakeford has announced that people from parts of the United Kingdom that have high rates of coronavirus will be prevented from travelling to Wales.
Mr Bleasdale said: "There will also be plenty of individuals travelling legitimately from areas which are not high risk, and this will only add to the other difficulties officers face when policing the existing regulations".
Rees-Mogg said the Senedd had imposed an "unconstitutional" border between England and Wales when it introduced a travel ban on people coming into the country from virus hotspots across the UK.
"This would be a short, sharp shock to the virus which could turn back the clock, slowing down its spread and buying us more time and vital capacity in the health service".
"A firebreak would also, however, be a short, sharp shock to all our lives". A report released Tuesday showed that the government's science advisers had urged his government to install much tougher measures, including a two- to three-week national lockdown. "The shorter the period, the sharper the measures will have to be".
But Alun Cairns, Conservative MP for the Vale of Glamorgan and former Welsh Secretary, accused Mr Drakeford of being "anti-English", despite the Welsh restrictions covering people from all United Kingdom nations.
It is not yet clear whether people will be issued with fines for breaking the rule.
No detail was given about what a new set of Wales-wide restrictions could look like.
"These are incredibly hard decisions and we have not yet come to a final conclusion about whether a firebreak is the best way to act", Mr Drakeford added.
"If it's so serious there should be an emergency recall of the Welsh Parliament on Monday and a statement given", he said.
First Minister Mark Drakeford said his government had fallen out with the Prime Minister over his refusal to act on the travel ban.
Earlier on Wednesday, Scotland's First Minister Nicola Sturgeon said she backed Mr Drakeford's calls for the UK Government to introduce travel restrictions on people in areas with high levels of coronavirus.
The First Minister said he could not give a guaranteed date for the travel ban to end, saying it would "depend upon the way that events and circumstances unfold over the next couple of weeks".
"I continue to be very grateful to the people of Wales for all the efforts they have made and continue to make".
"This week you will have seen that we've had quite a falling out with the Prime Minister over his refusal to act to protect low incidence areas of coronavirus from visitors from high incidence areas".
"The Prime Minister says to me he's issued guidance but the problem with that is the police can't take action on the basis of guidance".
"And if that unfortunately means people can't travel in the way they did before then that's got to be put in place".