The First Minister has said Wales could open parts of the economy earlier than in England.
Mark Drakeford said bringing Wales out of lockdown wouldn't automatically follow England despite all four nations having a "broadly aligned" approach.
"Broad alignment doesn't mean doing everything the same," Mark Drakeford told the Welsh Affairs Committee on Thursday.
"I think there will be some opportunities because rates in Wales are significantly lower than they are in England that we may be able to restore some economic activity earlier than the Prime Minister's road map currently suggests.
"I wouldn't want to deny businesses in Wales the chance to get back trading because we were waiting for somebody else to be in a position that we had already arrived at."
Welsh plans currently indicate that hairdressers and some shops may reopen on March while across the border, the PM does not plan to open hairdressers and non-essential shops until April 12.
The one-off session to discuss intergovernmental relations on a wide range of issues from Brexit to the coronavirus pandemic response was the first time Mr Drakeford had appeared before the committee and the first for a First Minister since 2015.
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Mr Drakeford, who is self-isolating, also told the committee how a "remote" relationship with the Prime Minister was hampering the way the country as a whole is being run.
He said he had only met the prime minister "once myself" and added: "The remoteness isn't just in that way, I'm afraid we rarely have a meeting of minds."
Mr Drakeford said: "The picture is very mixed: there are some places where engagement is good and some places where it falls far short of what would be properly expected. There are some areas where there have been improvements as well."
Since the New Year, there has been a "regular and reliable rhythm of meetings" between the UK Government and the First Ministers he said, which includes a weekly meeting with Michael Gove on a Wednesday evening.
The big problem remains in that it all takes place on a "relatively random basis" he added, with no "institutional architecture" to make the United Kingdom work.
"It is all ad-hoc, random and made up as we go along," he explained.
"If I have an anxiety about the lack of regular engagement between the Prime Minister and other parts of the United Kingdom, it is that without that the future of the United Kingdom becomes more difficult."
Wales or England - whose path out of lockdown is best?
Mr Drakeford also made a call for "home rule".
Referring to recent announcements from the UK Government such as the fact the Shared Prosperity Fund would be controlled by the UK Treasury, Mr Drakeford said he would like to see the areas where responsibilities of devolution currently exist at the Welsh level are set down "in a way that guarantees that they can continue and not interfered with in the way we have seen in recent months".
The effect of the pandemic in the past year had polarised opinion in Wales about the way the country should be governed, he said.
While the Welsh government has been criticised for not laying out a more detailed plan for exiting lockdown, Mr Drakeford said the different approach had created a greater impact in Wales in areas such as how PPE was sourced and distributed and the fact that the 2m rule was enforced as law rather than guidance only.
He also explained how the Welsh Government permitted health boards to start calling forward the next priority groups in the vaccination rollout when 50% of the group before had received their jabs.
"It's simply to make sure we never have vaccines going to waste," he said.
"Because as a category begins to be vaccinated, if you get down to a relatively small number of people still waiting then you don't have a pool of people who you can call in at short notice to make sure every drop of vaccine gets used."