Britain’s high military dependence on the US “is no longer tenable” and the UK has to become increasingly independent of the special relationship with Washington, a former Nato chief has warned.

Lord Robertson, who last week accused British leaders of a “corrosive complacency” towards defence, said on Wednesday the traditional allies were diverging over values – and that even after Donald Trump, the separation was likely to continue.

The peer, a former Labour defence minister and Nato secretary general, highlighted Trump’s unprovoked attack on Iran, his decision to levy tariffs on traditional allies and, “most jarringly”, the threat to wrest Greenland from Denmark.

“All of these illustrate a growing divergence between Westminster and Washington,” Robertson said at a seminar at the Chatham House thinktank. He said the diplomatic tone from the White House had “reached a historic low point” with Trump’s repeated public criticisms of the UK.

Trump’s unilateral actions during his presidency also indicated that the postwar era in which the US acted as a steward maintaining global rules, norms and institutions “may well be over”, he said.

Keir Starmer has offered limited military support to the US bombing of Iran, refusing to participate directly as questions remain over whether the initial attack that killed the country’s supreme leader, Ali Khamenei, was legal under international law.

That prompted Trump to compare Starmer to Neville Chamberlain, describe the Royal Navy’s aircraft carriers as “toys” and to complain that UK wants to help secure the strait of Hormuz only once “the war is over”.

Robertson emphasised that Trump did not represent the full spectrum of American opinion, but said the UK needed to accept the president’s behaviour was also reflective of longer-term changes in US foreign policy and act accordingly.

“It’s clear that our high level of military dependance on the US is no longer tenable,” Robertson said that it was a “naive belief” that the White House would always be on hand to help the UK out in times of conflict. Such an approach had led “to the diminishment of our own capability” militarily, he added.

He said the UK “must rapidly pivot to becoming a more autonomous military actor”, working closely with European allies against Russia, and demonstrate progress to lifting defence spending to 3.5% of GDP by 2035 in line with a Nato target, while recognising that the US was becoming more transactional.

“The relationship with the United States will depend very much on what we contribute to the alliance,” Robertson added, amid forecasts that Germany is on track to spend twice as much on defence as the UK by 2029 if both countries maintain their current plans.

It is the second time in a week that Robertson has intervened over military spending with comments that he hopes will strengthen Ministry of Defence’s hand in a long-running row with the Treasury. There remains an £18bn funding gap in a 10-year defence investment plan, leaving key commitments not yet signed off.

The peer’s remarks came after the cross-party Lords international relations and defence committee, which he chairs, published its own report on the special relationship. It concluded that the relationship was “under greater strain today than at any point since the second world war”.

Robertson did not comment on whether the disastrous appointment of Peter Mandelson by Starmer last year had worsened a declining relationship with the US.

Lord Darroch, a former UK ambassador to Washington and another member of the Lords committee, said at the same event that it was inevitable that prime ministers would sometimes try to make a political appointment to the post.

“As a diplomat myself, I like the idea the job should, more often than not, go to diplomats. The history of British diplomats in that job in Washington has been pretty favourable,” he said.

But he added that what politicians might occasionally want was someone whom they thought they could trust, adding: “It won’t be the last time this happens.”

Responding to the Lords committee report, Warren Stephens, the US ambassador to the UK, said the White House national security strategy made it a top priority to “support our allies in preserving the freedom and security of Europe”. The US would work alongside the UK, “our closest ally”, to keep both countries and their citizens safe and prosperous, he added.