In her 2015 speech to the Conservative conference, Theresa May declared: "We welcome students coming to study. But the fact is, too many of them are not returning home as soon as their visa runs out. If they have a graduate job, that is fine. If not, they must return home. So I don’t care what the university lobbyists say: the rules must be enforced. Students, yes; overstayers, no."

The belief that tens of thousands of students were overstaying their visas was used to justify their inclusion in the Conservatives' net migration target (aimed at reducing migration to "tens of thousands" a year). But two remarkable new studies suggest the claim is entirely false. A Home Office paper based on "exit checks" found that that 176,317 – 97.4 per cent – of of 181,024 foreign students left on time or had their visas extended. This compares with a previous estimate that as many as 100,000 overstayed.

A separate Office for National Statistics study similarly debunks the claim. Exit checks found that of those whose visas expired in 2016 and 2017, 69 per cent left the UK, while 26 per cent extended their visas for further study or for work. The remaining 5 per cent had no identified record of departure or extension, or appeared to depart after their visa had expired.

As the ONS concludes: "There is no evidence of a major issue of non-EU students overstaying their entitlement to stay". Some have suggested that the findings prove total net migration is far lower than thought, putting the Conservatives within reach of their target, but the ONS advises caution on this point: "There may potentially be some 'offsetting' with other groups of migrants who will contribute to the total net migration figures in other ways. For example, there could be a group of emigrants who have a tendency to understate their duration from the UK – perhaps British emigrants who return home earlier than intended."

Regardless of the true figure, the data debacle does not inspire confidence in the UK's ability to design a coherent post-Brexit immigration system. May will also face renewed pressure to remove foreign students from the net migration target (Home Secretary Amer Rudd has belatedly launched an inquiry into their economic contribution). As George Osborne's Evening Standard recently said: not one senior cabinet minister supports the policy.

Last July, Boris Johnson and Amber Rudd both suggested that the target should be abandoned before being rebuked by No10 (Rudd did not even reference it in her recent FT article on immigration). Philip Hammond and Liam Fox have publicly argued that students should be excluded from the total. In view of all this, the target is likely to depart No10 when May does.