Wales is currently in the midst of a two-week mini-lockdown, introduced while the UK Government was still using its tier system of restrictions for different areas of England.
The Welsh 'firebreak' will lift on Monday, by which point England will have moved into a four week nationwide lockdown, expected to start on Thursday.
It means that again there will no uniform rules between the two countries, an issue for those on the border whose lives involve both countries.
Travel restrictions will be lifted within Wales when the 'firebreak' ends but expected restrictions on movement within England mean that only essential travel across the border will be permitted – such as for work.
Wales First Minister, Mark Drakeford, said he expected people to follow the English rules, which would restrict travel across the border.
Asked about the potential for people to travel from England to Wales where shops and other parts of society will be open Mr Drakeford said: "They must obey the law in England and the law in England will not allow that to happen for very good reasons. The measures put in place in England are designed to turn back the scale of challenge that coronavirus is causing to our friends and neighbours across the border.
"Those rules will have been put in place by the Prime Minister for very good reasons and people in England need to follow them just as I always ask the people of Wales to follow the rules we have put in place here."
On the issues of crossing the border for work Mr Drakeford said: "People who live in Wales but work in England will have a reasonable reason for travelling to work and people who live in England and work in Wales will equally have a reasonable excuse for come across the border to work here.
"But it will be a restricted list of essential purposes rather than the normal to-ing and fro-ing across the border in less fraught and difficult times."
Under the Welsh Government plans for the end of the 'firebreak' two households can form a bubble and meet indoors in from Monday. Up to 15 people will also be able to take part in an indoor activity, and up to 30 people outside.
Mr Drakeford also said he was satisfied with the Welsh Government's decision to implement the 'firebreak'.
A similar measure had been recommended by scientists in England during September but was rejected by the UK Government.
He said: "The advice we had from our chief medical officer and our scientists was that we acted early and had a 17-day period that was short and sharp, and we have really asked an extraordinary amount of the Welsh people over these 17 days.
"The scientists told us that would be what we needed to turn back the tide of coronavirus in Wales and that is the decision we took, and was based on the science.
"We will stick to that because we think that is the best result for the people here in Wales in the circumstances we face."