DONALD Trump's attention turns to Eastern Europe on Tuesday when he meets Polish President Andrzej Duda. Yet, it was his landmark trip to Western Europe last week, configured around the 75th anniversary of D-Day, that has set the international political agenda in recent days.

The highlight of the US president's visit - last Thursday's Normandy anniversary ceremony aside - was a three-day trip to the United Kingdom amid a "transition of power" that could see kindred spirit Boris Johnson become prime minister.

Despite significant public protests, Mr Trump's tour was not the diplomatic disaster of last year, and both governments hope it may breathe new life into the 'special relationship' after his tricky ties with Theresa May who resigned on Friday as leader of the UK Conservative Party.

Mrs May was the first world leader to meet him in 2017 after he was sworn into office. At that time, Mr Trump called her "his Maggie", drawing comparisons with the intense political bond forged between Ronald Reagan and Margaret Thatcher.

Yet he and Mrs May have significant differences of political and personal approach, much larger than those between Mr Reagan and Mrs Thatcher.

While both leaders made efforts to seek a constructive partnership building on the traditional ties between the two nations founded on demographics, religion, culture, law, politics and economics, this ultimately fell flat and Mr Trump spent more energy last week engaging her potential successors, especially Mr Johnson who he effectively endorsed in just one of his breaches of diplomatic protocol.

Given Mr Trump's mercurial nature, a very big UK charm offensive was launched by the government and Royal family building on the pomp of last year when he visited Blenheim Palace (Winston Churchill's birthplace); Chequers (the countryside home of the UK prime minister); and Windsor Castle where he saw Queen Elizabeth.

The president, whose mother was born in Scotland, appears to value the close historical ties between the two nations, and appeared to especially enjoy seeing the Queen again and other royal family members last week.

SPECIAL RELATIONSHIP

It is clear that Mr Trump sees a potential, post-Brexit, US-UK trade deal as the cornerstone of a renewed "special relationship", and this could also be a boon for him personally given that he is criticised, in many quarters, as being an anti-globalisation, protectionist president.

From the standpoint of Brexiteers too, including Mr Johnson who is the current favourite to replace Mrs May in Downing Street, this would also represent a win in their own battle to show that the nation can potentially secure trade deals swiftly with key non-European partners.

There are key areas ripe for agreement here, including lowering or eliminating tariffs on goods. Equally, however, potential icebergs lie on the horizon, not least given the president's "America First" agenda.

Specific areas of potential disagreement on trade include the prospect that harmonising financial regulations between the two countries - with the international dominance of Wall Street and the City of London - will not necessarily be straightforward.

Meanwhile, securing agreement in other sectors, including agriculture, where there are divergences of views and strong interest groups, will not be easy.

Another key agenda item last week was security and defence which has long been at the core of the special relationship, as last week's D-Day anniversary highlighted, given the very close post-war partnership between the two nations in areas like intelligence. So while this is a terrain in which there will be much agreement, tensions surfaced, including over Huawei, the Chinese-headquartered technology firm, and Russia.

Take the example of Huawei where Mr Trump reportedly told UK officials that Washington may limit intelligence sharing if London allows the Chinese firm to build part of its 5G high speed mobile network given the security concerns he has about the firm. This decision, which will be a key one for Mrs May's successor, is a high stakes diplomatic balancing act for London given its desire to form closer post-Brexit economic ties with Beijing.

On Russia, Mr Trump has openly courted Vladimir Putin, despite Mrs May's repeated attempts, in the words of Mrs Thatcher, to seek to "stiffen his spine" against what she perceives as the real and present Russian security threat.

Whoever replaces Mrs May, the United Kingdom will likely remain a strong defender of Nato. In so doing, it is probable that the new prime minister will, under the UK's Article 5 responsibilities in that organisation, pledge to come to the aid of any Eastern European countries attacked by Moscow, an issue that Trump has so far been hazy on.

The US president appears to believe Russia is not a serious threat to the United States, and that there is scope for rapprochement with common interests over issues such as combating terrorism. Yet, even Mr Trump's own Cabinet colleagues, such as former US defence secretary James Mattis, have said that "Russia is raising grave concerns on several fronts", including trying to "break the Northern Atlantic alliance . . . which needs integrated steps - diplomatic, economic, military and the alliance steps. . . to defend ourselves where we must".

DIPLOMATIC GAFFES

While last week's trip featured many diplomatic gaffes from Mr Trump, including his criticisms of Prince Harry's wife Meghan Markle as "nasty", both sides are relieved it was not the disaster of last year's trip. Even by his own standards of disruptive diplomacy, that Summer 2018 UK tour was almost completely off-message with the US president seemingly undermining Mrs May at virtually every turn, including declaring the United Kingdom in "turmoil" following several Cabinet resignations in the week in question.

Given the multiple uncertainties ahead in the Trump presidency which could extend until 2025, the next UK prime minister is likely to seek to play the role of a trusted, albeit candid, friend in a bid to get close to the president to try to make the relationship work as smoothly as possible. This may provide some protections for bilateral relations in what could be a rocky few years of international relations to come, even if strong personal chemistry again fails to take root between the two leaders.

However, while this may be a sensible strategy, at least initially, it is not without risk, especially given Mr Trump's erratic nature and polarised standing in UK opinion. While seeking the potential upside in the new relationship, Mrs May's successor would be wise not to overestimate the UK's ability to shape US power, nor be blind to the fact that Mr Trump's America First outlook may - ultimately - care little for core UK interests, despite his avowed Anglophilia.