The former Labour leader said it was a “mistake” for the British Prime Minister to align herself so closely with Trump.
He instead welcomed Angela Merkel’s stance after the Chancellor advocated a partnership with the US only on the condition they adhere to the values Germany holds dear.
Miliband told Newsnight on Thursday: “Words and signals matter.
“They matter to the impact on Trump, who only respects strength, and they matter to our reputation around the world.”
May flew out to America on Thursday for a two-day trip that will see her become the first world leader to visit the White House since the billionaire tycoon’s inauguration.
Miliband said: “The tariffs that we have with the United States, they are incredibly low already.
“The thing that really worries me about this trade deal is that it goes towards... non-tariff barriers. What does that mean? Regulation.
“Regulation around health care, the environment, employee rights, and they have less regulation than us.
“So I think this trade deal is a really dangerous Trojan horse for which we seem to be locking ourselves in Donald Trump’s boot and I think that is not what I would be doing.”
Miliband added: “Our alliance with America should be based on our values, and the values we hold in common, not simply on the idea that we want to be at the front of some notional queue.”
JK Rowling joined Miliband and senior Tories on Thursday to warn May that “history” will judge her links to Trump.
The Harry Potter author tweeted her concern as Trump declared that torture of terror suspects “absolutely works”.
But although May and Downing Street insist that the UK does not condone torture, critics seized on Trump’s latest backing for ‘enhanced interrogation’ techniques for detainees.
Trump’s remarks sparked outrage and triggered a backlash against May’s own vow to work with him so the UK and US could “lead together again” on the global stage.
Miliband tweeted on Wednesday that “decent Tories” must “feel queasy”.
Sarah Wollaston, Yvette Cooper, Lord Paddy Ashdown and Sir Vincent Cable were also highly critical of May.
Trump said earlier this week that he is considering reopening the CIA’s so-called “black site” prisons, secret facilities around the world that were used to detain suspects in George W Bush’s “war on terror” before they were formally shut down by Barack Obama.
On the Presidential election campaign trail, Trump had supported “waterboarding”, a technique to simulate drowning that has been used by the US on terror suspects.
In his first major interview since becoming President, Trump cited so-called Islamic State’s atrocities against Christians and said “we have to fight fire with fire”.
“When they’re shooting, when they’re chopping off the heads of our people and other people, when they’re chopping off the heads of people because they happen to be a Christian in the Middle East, when Isis is doing things that nobody has ever heard of since Medieval times, would I feel strongly about waterboarding?” he said.
“I have spoken with people at the highest level of intelligence and I asked them the question ‘Does it work? Does torture work?’ and the answer was ‘Yes, absolutely’.