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."
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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.
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.
First Minister Mark Drakeford said: "I do think the effect of the pandemic and the last 12 months has been to polarise opinion in Wales about the way it should be governed.
"What we have to do - to quote a Conservative member of the Senedd, David Melding - is we have to recognise that the union as it is, is over. We have to create a new union.
"We have to demonstrate to people how we can recraft the UK in a way that recognises it as a voluntary association of four nations, in which we choose to pool our sovereignty for common purposes and for common benefits."
He added: "The idea that sovereignty is held only in one place and is handed out to other places, but always on a piece of string so it can be pulled back to the centre at any moment when the centre requires - I think that is over.
"I think 20 years into devolution, sovereignty has established itself in the different component parts of the UK and has to be regarded as dispersed. That doesn't mean disappeared from the UK Parliament - it continues to be there too - but it is not exclusively there.
"The European Union will be an example, potentially, but Canada, or Australia, or the United States are examples of what I talked about where sovereignty is dispersed amongst its component parts and pooled back together again for those central purposes.
"I think that simply describes the facts on the ground in the UK, in the third decade of the 21st century. That's how things are. Better to recognise it, better to put it purposefully to work for the sorts of purposes I would see us wanting to share, rather than attempting to deny that it has happened."
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."