It’s that moment again. When the opinion polls start to narrow in a general election campaign the Tories start to talk about immigration.

Theresa May was quick on Wednesday morning to seize on a leaked five-page Labour policy option paper given front page treatment in two Tory, attack-dog newspapers, the Mail and the Telegraph, to claim that a secret plan showed Jeremy Corbyn wanted “uncontrolled immigration” and was poised to “let in thousands of unskilled migrants from outside the EU”.

During a visit to Plymouth, she went on to claim that “too high, uncontrolled migration puts pressure on our public services, but it also lowers wages at the lower end of the income scale. I want to ensure that we control migration. Jeremy Corbyn and the Labour party want uncontrolled migration.”

But the Labour researcher’s short note was simply outlining an entirely legitimate option, which is simply the logical conclusion of any new immigration policy once Britain leaves the European Union. A special visa system to bring in low-skilled and unskilled labour from outside Britain is on every party’s immigration policy list, especially in shortage occupations such as wiping elderly Brits’ bottoms and picking fruit and vegetables.

Indeed, several government ministers, including the agriculture secretary, Andrea Leadsom, and the Brexit secretary, David Davis, have been pressing for the reopening of a scheme, known as the seasonal agricultural workers scheme, that has brought thousands of temporary, low-skilled migrants to Britain from outside Europe as recently as 2013. I am not sure May is accusing Leadsom and Davis of being in favour of uncontrolled migration.

As Jonathan Portes, professor of economics at King’s College London, has pointed out: “The policy described here is precisely that repeatedly floated by government ministers.” For example, Leadsom promised the Oxford Farming Conference on 4 January that British farmers would have access to tens of thousands of foreign workers through a system of temporary visas to pick fruit and vegetables post-Brexit.

Michael Howard. In 2005, he made immigration almost his whole general election campaign, and crashed to defeat. Photograph: Dan Chung/The Guardian

The existing, points-based immigration system, introduced by Labour in 2008, actually includes a route for employers to bring low-skilled migrants to Britain, known as tier 3. But it has never been opened on the assumption that free movement within the European Union would be enough to satisfy the demand for low-skilled labour by Britain’s employers.

It is therefore entirely logical that when the UK leaves the EU and freedom of movement comes to an end, it should be replaced by a scheme that allows employers to bring low-skilled migrants into Britain from inside and outside Europe. After all, some prominent leave campaigners promised that Brexit would mean an end to discrimination in favour of EU workers over those from Commonwealth countries.

There is a traditional moment in every election campaign when the Tories decide it is time to play the immigration card. In 2005, Michael Howard, then party leader, chose to make it almost his whole campaign with the slogan: “Are you thinking what I’m thinking?” Howard was surprised to find, as he crashed to defeat, that his 2005 campaign actually put off more voters than it attracted. Tory strategists may be gambling that is no longer the case.