Theresa May has criticised Boris Johnson’s immigration policy, warning that introducing a points-based system for prospective migrants is “not an answer to controlling immigration”.

In her first public attack on her successor, the former prime minister said Mr Johnson’s plans for such a system could “allow abuse to take place”.

She also voiced concerns about the government’s approach to imprisoning foreign criminals and considering regional visas for people to come to specific parts of the UK after Brexit.

Mr Johnson announced soon after taking office that he had asked officials to draw up plans for an “Australian-style points-based immigration system”.

It was seen as a move towards a more liberal approach than that proposed by Ms May’s government, which had wanted to significantly tighten immigration rules and proposed introducing a £30,000 salary threshold for people wanting to come to the UK.

The plans for the new system were included in the Queen’s Speech on Monday.

Speaking in the Commons during a debate on the speech, Ms May said: “I note that there have been many references recently to a points-based system of immigration. In 2010, when I become home secretary, one of the challenges I faced was dealing with the abuse that had arisen in the immigration system, largely enabled by the Labour Party’s points-based immigration system.

“It’s possible that the Home Office’s best brains have come up with a very good scheme, but I would simply urge the home secretary and the Home Office to look very carefully at the lessons that have been learnt in the past in relation to points-based immigration systems, which in themselves are not an answer to controlling immigration and can allow abuse to take place.”

Ms May also voiced concerns about the government’s plan to introduce tougher sentences for foreign criminals who breach deportation orders by returning to the UK, saying it would put additional pressure on UK prisons.

She said: “It is absolutely right to look at those cases where foreign national offenders, having been deported, are then brought back into the country, often illegally by criminal gangs.

“The issue I have, though, is that the result of the proposal is that we will potentially see more foreign national offenders in our prisons.

“The issue of dealing with foreign national offenders in our prisons is one that every home secretary is faced with when they come into office and I would urge the government, alongside what they’re doing, to look at seeing how we can most effectively remove foreign national offenders.”

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This should include “ensuring that we have prison transfer schemes, once we’ve left the EU, to replace those available to us within the European Union”, she added.

The former prime minister said she was also “concerned” about reports that the government could introduce regional visas to allow immigrants to work in specific areas of the UK where certain skills are needed after Brexit.