US President Donald Trump speaks prior to meet with Prime Minister Lee Hsien Loong of Singapore during a meeting

After having the threat hanging over him for what has felt like almost the whole of his presidency, Donald Trump now finally faces a formal impeachment investigation.

Nancy Pelosi, the Democratic speaker of the House of Representatives, announced that she was beginning the inquiry in response to allegations that the president was trying to recruit a foreign head of state to fabricate dirt on Joe Biden, the frontrunner to face Mr Trump in next year’s election.

In a statement she said: “The actions of the Trump presidency have revealed the dishonourable fact of the president’s betrayal of his oath of office, betrayal of our national security and betrayal of the integrity of our elections.”

It was a dramatic change of tack by Ms Pelosi, who has opposed efforts by her party colleagues to impeach the president.

But the controversy over Mr Trump’s mysterious July phone call to Volodymyr Zelensky, the efforts to keep a whistleblower’s complaint from Congress, and the suspicion that the president was trying to subvert American democracy - perhaps for a second time - served to change her mind.

The president himself punched back in characteristic fashion, unleashing a broadside of tweets that were by turn angry, insulting and boastful.

He reverted to some of his favourite catchphrases - “witch hunt”, “presidential harassment”; implied that efforts to hold him to account were tantamount to an attack on America - “so bad for our country”; and tweeted a re-election campaign video that featured him claiming that impeachment would help his poll numbers.

The impeachment process itself is likely to pass the lower chamber of Congress, the Democrat-controlled House of Representatives, where it needs a simple majority. But the Republican-controlled Senate, where a two-thirds majority is required for a conviction, looks virtually unattainable.

The Democrats will therefore hope that their dramatic gamble, 14 months before the presidential elections, pays off.