The White House announced Prime Minister David Cameron’s two-day visit to Washington in a statement issued last Saturday. It was a tellingly low-key announcement for an Anglo-American relationship that has mostly drifted in the past five years. The alliance, though, does have one big idea up its sleeve. Unfortunately, it’s a bad one.

It’s entirely possible that this will be Cameron’s last visit as Prime Minister to the US. In retrospect, the Cameron-Obama era will likely be one that historians will pass over with a bored shrug, like the shared tenures of Edward Heath and Richard Nixon.

That was an important era, but – unlike Kennedy and Macmillan, for example – it’s not one with compelling personalities who enjoyed working closely with each other on vital and shared interests. Even in the happier eras, the US and the UK didn’t always agree with each other, but then there was an urgent quality to the relationship that is lacking today.

For Heath, getting into Europe was more important than Nixon’s effort to get out of Vietnam, especially because he was the UK’s only post-war prime minister who positively disliked the United States. For Barack Obama, Europe is simply not a vital region of the world: he’s paid attention to it only when, as with Ukraine, it’s been forcibly brought to his notice.

The best that can be said about Anglo-American relations under Cameron and Obama is that it’s too soon to tell. If in a decade the Falklands are shivering under Argentine occupation, the Taliban are in Kabul, Libya is an Islamist stronghold and Assad is still in power in Syria, their time in office will have been a disaster.

Even today, we know that Obama’s regard for the UK is notoriously low. He has none of the appreciation for the Anglo-American tradition of freedom that marked predecessors like Reagan.

As a man on a mission to wind up the wars of Iraq and Afghanistan, his regard for the UK’s sacrifices there is limited.

He fought a war at France’s and Britain’s behest in Libya, only to find that the US had to do most of the actual bombing. And though he wasn’t eager to go to war against Assad in Syria, he was appalled that Cameron couldn’t deliver parliamentary approval for it.

Nor have the spies and lawyers been helpful. Traditionally, it was Britain that had the Communist spies, and the US that was over-run with lawyers. In the last decade, we’ve traded places: now it’s the US that can’t keep a secret, while the UK has increasingly become home to a carping community of international human rights lawyers.

But what has really marked the Anglo-American relationship since 2009 is its lack of grace. Obama is hardly alone among American leaders, but offences grow by repetition. As journalist Josh Rogin put it in commenting on the absence of senior Obama officials from the Charlie Hebdo march in Paris: “The Obama White House simply isn’t skilled, or doesn’t care, about doing the small things that can make a big difference when it comes to maintaining relationships and showing respect.”

The reason for this is that, as far as Britain goes, the White House doesn’t have a lot of respect to show. Nothing demonstrates this more clearly than the US attitude under Obama towards the European Union.

It’s quite true that Obama isn’t the first president to want to push the United Kingdom ever more closely into Brussels. But in earlier eras, the world seemed to be moving that way. After the end of Empire, entry into Europe looked – particularly in an era of bad British economic performance – to be the only logical choice. And broadly speaking, British public opinion moved from scepticism about the EU to disgruntled acceptance.

Today, though, British opinion is moving against the EU, just as the EU itself becomes ever more committed to saving the euro, even if it means dysfunctional and shrinking economies across the continent. The clash between the US establishment’s Europeanism and Britain’s desire to smell the free air outside Brussels has never been sharper.

That’s why the first two items on the White House’s announcement of Cameron’s visit were economic growth and international trade. The big agenda item going forward is the Transatlantic Trade and Investment Partnership, or TTIP, between the US and the EU. Often described as a free trade deal, TTIP would likely eliminate tariffs, which would be a good thing.

But it will also take the EU global, by harmonising the rules that stifle its growth with those in the US (where we’re also pretty good at making rules). The EU likes this, obviously. So does Obama: it combines his love of administrative rule-making with his admiration for the EU.

And Cameron likes it too. It sounds good, it will make big business happy, and it offers yet another rotten argument for staying in the EU: if Britain exits, it’ll supposedly miss out on the US market. In reality, it’s another attempt to get the economics of Britain’s EU membership to trump its politics, and to stick a spoke in the wheel of his Eurosceptic critics.

So Cameron’s visit may be low key. But low-key is not the same as low stakes.

– Ted R. Bromund is a senior research fellow at the Heritage Foundation’s Thatcher Center for Freedom.