Foreign student numbers in Britain will reach 600,000 a year by the 2020s, Theresa May has said, amid concerns over her plans to expel non-EU graduates.

Mrs May has faced criticism, including from inventor and entrepreneur Sir James Dyson, whose firm has its HQ at Malmesbury, after saying she wants the Conservative manifesto to include a commitment to compel students from outside the EU to leave the UK once they have completed their degree. They would then have to apply for a new visa if they wish to return.

Sir James said today the Government should be encouraging the brightest graduates to remain in the country and develop their ideas for the benefit of the British economy.

Speaking in the Commons, Tory backbencher James Gray (North Wiltshire) told Mrs May: "I strongly support the work you have done with regard to controlling bogus student visa applications. There was a huge regime that you've got rid of.

"However, how would you answer my constituent Sir James Dyson, who argues that if your latest remarks about automatically sending all students home on completion of their studies were to be taken literally then that'd have dire consequences for businesses like his who rely on engineers, scientists and others from overseas?"

Mrs May replied: "I say to you we have been very clear in all the changes we have put into the immigration system that we welcome the brightest and the best into the United Kingdom, we have no limit on the number of people who are coming here genuinely to study at a proper educational establishment and I'm pleased to say that visa applications from university students rose by two per cent in the year ending September 2014, with an increase of four per cent for the Russell Group universities.

"But we also need to recognise that the latest survey showed that in one year 121,000 students came in from overseas and only 50,000 left in that year and figures suggest that in the 2020s we will see 600,000 overseas students each year in this country."

Shadow home secretary Yvette Cooper claimed Mrs May's own party had backed away from her proposals to expel non-EU students at the end of their courses.

In testy Commons exchanges, Ms Cooper said: "James Dyson has called your new plan to expel overseas postgraduates short-sighted and said it would lead to long-term economic decline.

"The former Conservative universities minister (David Willetts) has said it is mean spirited and will damage our exports as well as universities.

"Even Conservative central office backed away from your policy yesterday.

"So do you stand by your plan and do you believe that overseas graduates should all have to return home before they can even apply for a high skilled job in British science or the NHS? Yes or no?"

Mrs May replied: "I'm very clear that the policies that we have are the right ones, that they ensure that we have the brightest and the best coming here to the United Kingdom.

"We do of course want to see people who wish to come here... at proper educational establishments.

"What we have been doing as a Government is clearing out the abuse that was allowed to run rife in this area of student visas under the last Labour government, so that we've seen 800 colleges no longer able to take in overseas students.

"We want to see the brightest and best coming to the UK and that's exactly what our policies are destined to do."

Ms Cooper said Mrs May had ducked the question.

The Labour frontbencher said: "I hope that means you are backing away from this policy, I hope this means this was simply a proposal from your special advisers and that is obviously why they have been banned from the Tory candidates list."