Lord Mandelson has hailed this week's UK-US trade deal a "platform for going further and opening up more trade opportunities", in his first interview taking up his role as the UK's ambassador to the US.
The deal has reduced or removed tariffs that were recently impposed by US President Donald Trump on some of his nation's imports from the UK, including cars, steel and aluminium.
Former New Labour cabinet member Lord Mandelson has played a crucial role in negotiations between the two nations since he started his job in February.
Speaking to BBC Two's Newsnight he said he was "looking forward" to further agreements to bring "down further tariffs".
On Donald Trump's self-declared Liberation Day in early April he announced that the UK would be subject to 10% tariffs on the all the goods it exports to the US. More stringent measures were later applied to cars, steel and aluminium.
But on Thursday, the US agreed to allow some steel and aluminium into the country tariff-free, and reduced the levies on a set number of British cars.
Since then, Prime Minister Sir Keir Starmerhas said there are "ongoing discussions" with the US over the UK's own Digital Services Tax (DST) - a 2% levy that raises about £800m a year mainly from US tech companies.
Lord Mandelson said it was discussed during the latest round of negotiations between the two nations but he said "abolishing" the DST had not been part of the trade deal.
"If the Americans want to come back and discuss the digital services tax, it's up to them," he said.
"What they suggested wasn't acceptable to us, so it's not in the deal," he explained.
White House trade adviser Peter Navarro said on Thursday that President Trump's administration was still pressing the UK to lift the tax, referring to it as a "bad virus".
He told reporters at the White House: "We're still in negotiations...that's a very big deal to President Trump."
When asked by Newsnight's Matt Chorley about his observations on the relationship between Starmer and Trump, the ambassador said that while they were "not cut from the same cloth... they do both stand up for and defend their national interests".
He continued: "And where they see those interests converging or whether they've got to be made to work well, they set their minds to achieving that, and they do it very well.
"They do it by talking well to each other, very straightforwardly. They have trust in one another."
Lod Mandelson explained that this makes Starmer a prime minister "who's going to stand up for Britain internationally, who's going properly to explain and defend our national interest... [and] maintain good relationships" with close allies.
He said that following the UK-US deal, he had received "a lot of messages from fellow ambassadors here in Washington saying, 'congratulations, wish we were in the same position, how did you do it?'"
He added: "So that's something, that's a feather in our caps and something you and others, if I might suggest, should celebrate."
On his own relationship with the US president, Lord Mandelson said when he first walked into the Oval Office, Trump said "God, you're a good looking fellow, aren't you?".
The ambassador described Trump as a "people person" who takes people at "face value", explaining that the president judged him on his merits.