Boris Johnson has rejected a demand from the first minister of Wales for a travel ban in and out of Covid hotspots in England.
“There are no physical borders between Wales and England,” the prime minister’s official spokesman said.
He said guidance was “very clear” that people from very high risk areas such as Merseyside “should avoid travelling in or out of the area”.
Mr Drakeford has threatened to take action if a ban is not imposed.
The news led to a call from Plaid Cymru for the Welsh Government to act in light of the refusal.
Meanwhile on Tuesday the first minister said there should be an “extra special” Cobra meeting held to discuss a so-called “circuit-breaker” lockdown.
Welsh ministers have asked for travel from areas with high rates of coronavirus in England to be restricted, to prevent people visiting parts of Wales where lockdowns are not in force and where infection rates are lower.
It is the second time the UK government has said it would not agree to the Welsh Government’s request.
Seventeen areas of Wales - 15 counties, one town and one city - are currently under local lockdown restrictions, preventing travel in and out of them.
Mr Drakeford wrote to Mr Johnson on Tuesday saying efforts in Wales “are being undermined by travellers from high-prevalence areas in other parts of the UK travelling to Wales”.
He attached a scientific paper which he said “demonstrates the spread of infection geographically and supports the case for travel restrictions as a means of controlling the spread of the virus and avoiding seeding events in areas of lower prevalence”.
The paper, seen by BBC Wales, concludes that the “easing of lockdown rules into August has corresponded with an increase in cases [in Wales], which may partly be driven by imports from other parts of the UK and wider world”.
The paper adds that cases “in less urban areas” are “more likely to be imports from elsewhere and rarely lead to local onward transmission”.
But the paper also adds the data “does not constitute definitive proof”.
UK government sources were told the paper had not been peer-reviewed enough to be published.
‘I will act’
Mr Drakeford said he was writing to the first ministers in Scotland and Northern Ireland and asking them to regulate travel in a similar way.
“It would be better if all four nations were to act in concert, but in the absence of an agreed way forward, I will act to keep Wales safe,” he said.
A number of UK government sources say without data or evidence to prove people travelling from lockdown areas in England has led to an increase in Covid-19 cases in Wales, they are unlikely to change travel restrictions from guidance into law.
Plaid Cymru leader Adam Price said the UK government “has shown utter contempt for Wales, our people and our democracy.
“The time to ask is over. Now is the time to act.”
“There are no physical borders between Wales and England,” the prime minister’s spokesman said.
“What we have done is publish guidance which is very clear that people from very high risk areas such as Merseyside should avoid travelling in or out of the area.
“We have also made it very clear to the public that they should follow any local guidance which is issued by devolved administrations.”
The first minister said in the Senedd he has asked the prime minister for a special Cobra meeting to discuss a “circuit breaker” system - imposing a short period of restrictions for everyone - for dealing with coronavirus.
The UK government’s Sage advice group called for a short lockdown three weeks ago.
Mr Drakeford said the Welsh Government’s Technical Advisory Cell (TAC) had not yet advised ministers to implement such a system in Wales “but I do take the arguments in favour of a circuit breaker period seriously”.
“I think it’s an idea that will need further examination and needs to be shared in perspective between the four UK nations,” he said, adding the request was in Tuesday’s letter.
Mr Drakeford added that his call for a travel ban was not “some sort of contest between Wales and England”.
“This is not about stopping people from England coming to Wales, nor should we ever fall into that sort of way of talking,” he said.