It’s fair to say that today’s Prime Minister’s Questions won’t be featuring in Jeremy Corbyn’s highlights reel. Theresa May agreed to publishing a White Paper on Brexit before he stood up, and he had to improvise the first question, and thereafter never really regained his momentum.

But he had one question that has the potential to drag May and her government into the mire. While she did a good job sidestepping it today, she won’t be able to avoid it forever.

It was this: can the government commit that a trade deal between the United States and the United Kingdom won’t open up the National Health Service to exploitation by American corporations?

May was able to bat it off by talking about the government’s commitment to funding Britain’s health service and the increase in the minimum wage. And as far as the cut-and-thrust of PMQs is concerned, she’ll be able to do that.

But sooner or later, an actual trade deal between the United States and the United Kingdom is going to be on the floor of the House, and rhetorical flourishes about the Conservatives’ record since 2010 won’t do much good.

The government faces two headaches in particular as far as a trade deal between itself and the United States are concerned. The first is the NHS, which has the potential to cause public unease on a par with the row over Andrew Lansley’s NHS reforms which, we shouldn’t forget, knackered the government for over a year. And don’t forget either that the Coalition had a majority of 77 while the government has one of just 11.

The second – and potentially the more explosive, despite the emotional hold the Health Service has in British politics – is over agriculture. There are two major stumbling blocks: the first is genetically modified food, commonplace in the United States but the subject of a greater level of controversy throughout Europe, including the United Kingdom. The second is what is given to livestock – that is, what is fed to our cows, sheep, pigs, as well as the hormones that are pumped into them. There are far higher restrictions on what you can do to your livestock in British farms than there are in the United States.

That risk comes in two shapes for the government. The first is a consumer panic about what goes into our food. But the more acute as far as the government’s ability to legislate is concerned are the worries of Conservatives in farmland constituencies that were either Liberal-held or had the Liberal Democrats second in 2015. A deal with the United States is going to be much more politically fraught than many expect – and not only because of the NHS.