What is the best way to respond to Donald Trump and his sweeping tariffs? Keir Starmer thinks the answer is to tread softly, softly – while engaging in intensive negotiations behind the scenes.

There are signs that this strategy is bearing fruit. On Wednesday night, the president announced “reciprocal tariffs on countries throughout the world” including a 10% import tax on UK exports to the US – crucially, lower than the 20% imposed on the EU. The 10% rate was the lowest rate Trump announced and applied to several other countries including Australia, Singapore and Brazil.

It is a sign that the prime minister’s lovebombing campaign – including an invitation to Trump to meet King Charles in June – has put the UK in good stead. There will be no great sigh of relief inside government, however. The 10% tariff is bad news for the UK economy (as are the US tariffs more broadly) and Starmer’s priority will be to negotiate its reduction or withdrawal.

Ministers have been unsuccessful so far in their efforts to sign an economic deal with the US by offering concessions on taxes for big tech firms and lower taxes on meat and fish imports. By Wednesday morning, No 10 was resigned to the fact that the UK would not be exempt from the wave of tariffs, which Trump announced in the White House Rose Garden in an act of political theatre and unabashed projection of his power on the world stage.

There are reasons for Starmer to be optimistic as his focus shifts to inking an economic deal within weeks or even days. Leslie Vinjamuri, the director of the US and Americas programme at Chatham House, said that so far the UK had “played its hand extremely well” and “one can imagine a scenario where that US-UK deal is announced pretty quickly”.

Vinjamuri said Trump had “boxed himself into a corner” where he had to announce universal tariffs before negotiating country by country but that there were signs the UK would be at “the front of the queue” for a deal.

“If the UK decides to roll back the tax on America’s tech firms that will be a huge win and, for the president, far better to announce that after he’s levied a punishment,” she said, adding that ministers could “lace it up with a visit to Scotland by Trump to meet the king”.

Others argue that Starmer’s approach is fraught with risk, however, by unnecessarily drawing Trump’s attention to the UK – which could lead him to exact concessions that wouldn’t otherwise have needed to be made.

David Henig, a trade expert, said Starmer’s approach was “in one sense softly-softly not threatening, in another quite aggressive in seeking a deal, when that could cast a spotlight on perceived UK faults when we weren’t otherwise in the firing line”. He said the risk was that the US administration could target areas such as the UK’s digital safety laws, food standards or VAT.

Government officials said an economic deal with the US is broadly ready and could even be finalised within days. The success of Starmer’s approach will be judged by how quickly that happens – South Korea, Japan, India and Australia have all been trying to strike similar deals.

Jonathan Reynolds, the trade secretary, said the government’s approach would be “to remain calm and committed to doing this deal, which we hope will mitigate the impact of what has been announced”.

The EU, meanwhile, has vowed to respond with “robust” retaliatory tariffs against the US. Starmer has come under pressure from some quarters to harden his own approach. Ed Davey, the Liberal Democrat leader, called for the UK to form an “economic coalition of the willing” with the EU and Canada to counter Trump’s “divide and rule” tactics.

For the prime minister and his team, including the foreign secretary, David Lammy, the settled strategy is to follow the approach set by the former Japanese prime minister Shinzo Abe. Abe established a good rapport with Trump during his first term thanks to some carefully choreographed flattery and behind-the-scenes diplomacy.

“The hard-edged singular focus on retaliation is misplaced. It assumes that by retaliating you win but everybody loses,” Vinjamuri said. “One doesn’t want to be prescribing that America’s allies and partners become overly sycophantic, but there is a lot to play for and there is a lot to win.”