Labour has been working hard to win over Donald Trump in case he is re-elected, Health Secretary Wes Streeting said.

Polls have opened in the US for Americans to start voting in what is set to be a neck-and-neck race for the US presidency between Kamala Harris and Mr Trump.

Sir Keir Starmer will have rocky terrain to navigate if Mr Trump wins, in part due to scathing criticism that current Cabinet ministers made of the Republican politician while Labour was in opposition and because of a row over Labour Party volunteers who travelled to the US to support the Harris campaign.

The Health Secretary was asked about a 2017 post on social media in which he called Mr Trump an “odious, sad, little man”.

“The Prime Minister and the Foreign Secretary have been working hard to build a relationship with President Trump and his team, so that in the event that he is elected as the next president of the United States, we start with the strong working relationship which is in our national interest and in the interests of the United States as well,” he told Good Morning Britain in response.

Mr Trump had a “very good meeting with Keir Starmer not too long ago” and “of course, he’ll be aware of things that we’ve we’ve all said in the past”, Mr Streeting added.

He said that Foreign Secretary David Lammy, who has called Mr Trump a “neo-Nazi-sympathising sociopath” in the past, has strong relationships with people around the former president, including his vice presidential nominee JD Vance.

Though Labour and Mr Trump “may not be ideological bedfellows”, if he is elected “there will be a really good working relationship”, the Health Secretary told LBC.

He pointed to Reform UK leader Nigel Farage, who attended a rally in the US on Monday night in support of Trump.

“[Mr Farage] was reflecting overnight that whatever some of the noise we’ve heard about, you know that legal action or indeed things that we said about President Trump in the past, that we’ll be able to work effectively together as partners and and as allies.”

Mr Farage meanwhile said he rated Joe Biden’s presidency as “catastrophic” and Ms Harris’s vice presidency as “nul points”.

“She’s a terrible candidate,” he told LBC about the Democrat hopeful.

A Harris campaign win would be the favourable outcome for the UK, according to an expert on US affairs, while under a second Trump presidency the UK would be faced with a “tougher ask”.

The Republican candidate is likely to chart a new US course on major conflicts in Ukraine and the Middle East, areas where Sir Keir has largely followed the lead of US President Joe Biden.

“Donald Trump will have a much tougher ask,” Dr Leslie Vinjamuri of Chatham House told the PA news agency, claiming the Harris campaign would be a preferable partner to Sir Keir’s Government.

Dr Vinjamuri, the director at the influential think tank’s US and Americas programme, added: “I don’t think that he (Mr Trump) puts the same emphasis on the history of co-operation and partnership and alliance as we’ve seen from the current Biden administration, or as we would likely see from a Harris administration. He’s much more transactional.”

Mr Trump would likely push European Nato members to aim for 3% of GDP (gross domestic product) spending on defence, she told PA, an area where the UK is currently predicted to spend some 2.3% of GDP in 2024 while it grapples with ailing public finances.

Republican candidate Mr Trump is also likely to push for a peace deal between Ukraine and Russia, upsetting commitments by European leaders – including Sir Keir – to Volodymyr Zelensky’s war efforts.

Dr Vinjamuri said Mr Trump will also want to “play a significant role” in transforming the Middle East, likely in a strong pro-Israel manner that may clash with Sir Keir’s pro-Gaza leaning political base, as well as the UK’s stated position that a two-state solution is the preferred outcome to the conflict.

“The bottom line, if there’s a Trump administration, is on the security front there is going to be a demand to spend more and to line up,” Dr Vinjamuri said.

A Harris presidency would be more likely to value the long-standing UK-US relationship as “trusted allies”, the expert said, but added there was no guarantee she would be a continuity Biden figure due to the “transitional” period of conflict and turmoil across the globe.

Sir Keir has drawn the ire of some Republicans in recent weeks. The Trump-Vance team has filed an official complaint with US federal electoral officials after reports that Labour Party officials met the Harris campaign and volunteered for her.

The Prime Minister has insisted this is no different to similar co-operation in previous elections and has sought to build links with both candidates, meeting Mr Trump in New York in September.

Efforts to smooth over the relationship should Mr Trump win will unlikely be aided by a royal charm offensive, Dr Vinjamuri said.

“Trump had a deep affection and deep sense for Her Majesty the Queen, and that actually really mattered a lot. It helped a lot with the US-UK relationship,” she said.

She added: “There’s no sense of that continuing or being transferred to the King, which isn’t to say that Donald Trump has any antipathy, but there’s no apparent sense of just deep admiration in the way that he so clearly had for the Queen. And so you take away that kind of, that one thing that really did matter for Donald Trump, did sort of tame him, and I think it’s a very different proposition.”

Both Mr Trump and Ms Harris have made their final campaign push with American voters in so-called swing states such as Arizona, Georgia and Pennsylvania, where the race is expected to be close.

Under the US voting system, a total of 270 votes in what is known as the electoral college are needed to win the presidential election.

Ms Harris narrowly leads Mr Trump in the final prediction by YouGov ahead of the US election, with the pollster predicting she has 240 electoral votes, Trump 218, while a further 80 remain uncertain.

Key issues in the race to be the next US president include security on the US’s southern border with Mexico, abortion rights and reducing inflation.