Bolton dangled a separate trade deal between Britain and the US once Britain rids itself of the EU, saying "we are ready to go".
The commentary from members of Trump's inner circle was an extraordinary departure from the diplomatic norm, in which close allies such as the US and Britain are careful not to appear to be meddling in each other's business.
Trump jnr said the Brexit process should be over by now and that May erred by not taking his father's advice on how to sever ties. May has said that Trump advised her to sue the EU rather than enter into what became protracted negotiations.
The younger Trump has not previously commented extensively on foreign policy. Bolton supported Brexit before becoming Trump's national security adviser a year ago and shares the President's view that the EU impinges on state sovereignty.
"God bless the people of Great Britain, who two years ago voted to get out of the European Union," Bolton said in a speech last year.
Bolton is known to speak with pro-Brexit British ministers. He told Sky News that British trade secretary, Liam Fox, a vocal Brexit supporter, "would be welcome here" for talks on a separate US-UK trade deal once Britain is out of the EU.
An agreement could be reached "quickly," Bolton predicted, although such a pact faces an uncertain and probably lengthy review in Congress, where Democrats and Republicans have expressed reservations.
"The president's been clear that he wants a resolution to this issue that allows the United States and Britain to come to trade deals again," Bolton said.
He added, "The people of Britain have voted. When is the political class going to give effect to that vote?"
Britain's Parliament has twice rejected May's plans for departure. She conceded today that she must ask EU leaders to delay Brexit until June 30, and blamed MPs for foiling plans to exit on schedule by March 29.
There is no agreement in place governing British trade and the border between Ireland and Northern Ireland, and May wants to prevent Britain from "crashing out" of the EU without those safeguards.
Senator Chris Murphy, D, was in London attempting, he said, to reassure Britons that Trump jnr's "bonkers" opinion piece may reflect the President's views but is not a stand-in for official US policy.
"The Donald Trump jnr op-ed has completely flummoxed people over here," Murphy said in an interview. "It sounds like it was written by [pro-Brexit politician] Nigel Farage, and people don't know if it's official US policy or just an op-ed the pro-Brexit crowd handed to the President's son to submit to a newspaper."
Tony Travers, a professor of politics at the London School of Economics, said Trump jnr's article symbolised "part of the willingness on both sides - leave or remain - to use any weapon at all in defence of their position."
He noted that Trump's team would have calculated, rightly, that the Daily Telegraph is among the most pro-Brexit newspapers in the country. But he said there was little resentment over the piece, in part, because the US does not have a direct stake in the negotiations and because those who wish to remain are, on the whole, more moderate in their reactions.
"I don't think there is any sense of resentment about Donald Trump jnr writing in the Telegraph in this way," he said. "Oddly, there would be have been more resentment if an Irish or Dutch or French politician had written something. Having an American political figure step into this will make some pro-Brexiteers feel comforted. Some like Trump quite a lot."
