The 25 per cent levy on steel, along with a 10 per cent tariff on aluminium, will come into effect tomorrow.
An exemption first granted to the EU, Mexico and Canada by Mr Trump in March is expiring and not being renewed.
European Commission president Jean-Claude Juncker denounced the move as “protectionism, pure and simple”. A UK Government spokesman described the move as “deeply disappointing”.
The Confederation of British Industry (CBI) warned the move would “damage prosperity on both sides of the Atlantic”.
Industry body UK Steel said with exports to America worth half a billion dollars a year, producers in Britain would be “hit hard”.
The EU will now take action against the US at the World Trade Organisation, while imposing duties on American imports expected to include orange juice, peanut butter and other goods.
Trade commissioner Cecilia Malmstrom said that throughout negotiations stretching over the past months, the US had tried to use the threat of trade restrictions “as leverage to obtain concessions from the EU”.
“This is not the way we do business and certainly not between long-standing partners, friends and allies,” she said.
Speaking from Paris, US commerce secretary Wilbur Ross said talks with the EU had made “some progress”, but not enough to extend the exemption. He stressed Washington was “willing and indeed eager to have further discussions”.
A UK Government spokesman said as close allies of the US, Britain and other EU states should be “permanently and fully exempted from the American measures on steel and aluminium”.
“We have made clear to the US Government at the highest levels the importance of UK steel and aluminium to its businesses and defence projects,” the spokesman said.
“We will continue to work closely with the EU and US administration to achieve a permanent exemption and to ensure that UK workers are protected and safeguarded.”
UK Steel director Gareth Stace said: “President Trump had already loaded the gun and today we now know that the US administration has unfortunately fired it and potentially started a damaging trade war.”
The new tariffs will cause “damage not only to the UK steel sector, but also the US economy”, Mr Stace said. He added: “With some half billion dollars of steel exported from the UK to US last year, UK steel producers are going to be hit hard.”
The CBI’s international director Ben Digby said: “The President’s measures are deeply concerning for firms in the UK, for close trading partners and across supply chains.
“There are no winners in a trade war, which will damage prosperity on both sides of the Atlantic. These tariffs could lead to a protectionist domino effect, damaging firms, employees and consumers in the US, UK and many other trading partners.”
Labour spokeswoman on steel Gill Furniss described the tariff announcement as “a catastrophic blow to the sector and steelworkers across the country”.
“Theresa May and her Government have approached the ongoing crisis with utter complacency and have proved too feeble to stand up to Trump when it was most needed,” said the Sheffield Brightside MP.
“They have let our steelworkers down.”