The United Kingdom's campaign to secure a free-trade deal with the United States shifted gear on the weekend when Prime Minister Boris Johnson spoke with Joe Biden for the first time since his inauguration as president.

Pundits had predicted the relationship between Washington and London could turn chilly because of Johnson's perceived closeness to former president Donald Trump.

But Downing Street insisted after Saturday evening's 35-minute phone call, which was instigated by Biden, that the two leaders were looking forward to "deepening the close alliance" between their nations.

After the call, Johnson tweeted: "Great to speak to President Joe Biden this evening. I look forward to deepening the longstanding alliance between our two countries as we drive a green and sustainable recovery from COVID-19."

The prime minister's office said they talked about trade, Biden's decision to rejoin the Paris agreement on climate change, and his plan to resume support of the World Health Organization.

The Guardian newspaper quoted a spokesman for Johnson as saying: "The prime minister praised President Biden's early action on tackling climate change and commitment to reach net zero by 2050."

The spokesman said they also discussed building "on the UK and US' long history of cooperation in security and defense".

Crucially, the spokesman said they "also discussed the benefits of a potential free-trade deal between our two countries".

"The prime minister reiterated his intention to resolve existing trade issues as soon as possible," he added. "The leaders looked forward to meeting in person as soon as the circumstances allow."

The BBC noted that Johnson said Biden's election success was a "step forward" for the US.

Johnson is understood to have been the first European leader to have had a call returned since the president's inauguration on Wednesday, possibly signaling the esteem Biden affords the UK, despite the fact that he was strongly opposed to the UK exiting the European Union.

A White House statement said Biden "conveyed his intention to strengthen the special relationship" between Washington and London and to "revitalize transatlantic ties".

Chris Mason, the BBC's political correspondent, said the order in which a new president speaks to other world leaders is usually seen as an indication of the closeness of the nations' bond.

"It is a crude metric of relative importance, but a metric nonetheless," he said.

But the Financial Times warned that the fact that Biden clearly showed Johnson and the UK respect by reaching out so soon does not necessarily mean a free-trade deal is on the horizon.

The paper said experts have suggested trade deals and other pacts are low on Biden's list of priorities.

The paper quoted Janet Yellen, Biden's nominee for the role of Treasury secretary, as saying the president wants to improve the US economy before he starts removing trade barriers.

"President Biden has been clear that he will not sign any new free-trade agreements before the US makes major investments in American workers and our infrastructure," she said.