Labour leader Sir Keir Starmer has said different approaches across the four UK nations to tackling coronavirus are not going to “help us out of this crisis”.
He blamed Prime Minister Boris Johnson for the way Wales and England had diverged in the easing of the lockdown.
Sir Keir said it reinforced his call for “radical federalism” across the UK.
But Welsh Secretary Simon Hart has said there were “far more similarities than differences in the approaches of the nations of the UK”.
Talking to the BBC’s Politics Wales programme, Sir Keir said there had been an “incredible sense of solidarity” across the United Kingdom, but the relationship between Wales, England, Scotland and Northern Ireland “could” be put under strain if there was an increasing divergence in approaches from the respective governments to coronavirus.
“The sooner, frankly, we get back to operating as four nations together the better,” he said.
“I do think responsibility for that lies very largely with the prime minister, who I would have hoped could have got all the ducks in a row before he actually made his speech last Sunday,” Sir Keir added.
In his televised address that day, Boris Johnson announced guidance that said people – in England – could “drive to other destinations” for exercise and leisure.
In Wales, the Welsh Government restated people cannot travel “a significant distance” from home for exercise.
Wales’ First Minister Mark Drakeford has told the BBC’s Political Thinking with Nick Robinson podcast he was not consulted before the UK government altered the lockdown slogan from “Stay at home” to “Stay alert”, adding that there was no change to the message in Wales.
Welsh Secretary Simon Hart has said: “No one part of the UK could face this pandemic alone and the UK Government has provided unprecedented support to every part of the UK.
“We entered this fight as a United Kingdom and we will come out of it equally united.”
In the BBC Wales interview, Sir Keir was asked whether it was politically difficult for him to criticise the UK Government’s coronavirus response on issues which had also troubled the Welsh Labour government.
He said: “I’m constantly asked to compare and contrast… and I’ve refused to get into that because I don’t think people want to hear that.
“What I’ve said is that the Labour party, certainly in the UK Government, will be a constructive opposition and what I meant by that is having the courage to say we’ll support the government when that’s the right thing to do.”
On Thursday, Sir Keir held online question-and-answer sessions with groups of Welsh voters in an attempt to understand the reason why Labour suffered its worst general election result in Wales since 1983.
He said Brexit and Jeremy Corbyn’s leadership had been issues for voters, but he believed “they were talking about something much deeper, about trust and engagement from the Labour Party”.
Sir Keir added that the “perception that the leader of the Labour party and Welsh Labour are in two different places, is not right, and that’s my job to make sure people realise we’re all on the same page, all working together”.
During the Labour leadership contest, Sir Keir said devolving more powers to the Welsh Parliament so that “more powers are closer to people” was the way forward.