Tony Blair's foreign secretary launched a withering attack on 'vile' Trump
Trump was elected on Wednesday after unexpectedly winning a string of key battleground states, and will take over from President Obama in January.
Beckett, a Labour party grandee who was foreign secretary under Tony Blair from 2006 to 2007, told Sky News that his election to the US presidency had left her feeling "horrified and terrified."
"I'm not just talking about the way he treated Hillary Clinton," she said. "Look at the way he treated his opponents in the Republican primaries. He insulted them, he sneered at them, he told lies about them, he insulted their families. This is a horrible man."
"Let's hope he was pretending and, in reality, he is this nice sweet person I'm sure we'll all be hearing about in the next few days," she said.
Beckett added that the billionaire had "appealed to the worst in everybody's nature, and brought it out and encouraged it."
"This is a man who when someone heckled at a rally called on his supporters to beat him up. He called for Hillary Clinton to have her security guard taken away.
"He even insinuated that people who didn't agree with her about gun control should perhaps think about shooting her. What kind of a man is that?" she said.
The reaction from UK politicians to Trump's shock victory has been mixed. Prime Minister Theresa May was quick to offer her congratulations to the president-elect for winning a "hard-fought campaign," and Foreign Secretary Boris Johnson said he was "looking forward to working with his administration on global stability and prosperity."
Positive reactions from Labour MPs, however, have been less forthcoming. Party leader Jeremy Corbyn said that Trump's success reflects "a rejection of a failed economic consensus" but added that "his answers to the big questions facing America are wrong."
The party's Scottish leader, Kezia Dugdale, refused to mince her words, and said that Trump was "responsible for a hate-filled campaign that was dominated by lies, misogyny and racism."