HANGZHOU, China (Reuters) - British Prime Minister Theresa May said she wants a new system to give the government control over who is able to enter the country after it leaves the European Union, rather than a points-based system that selects candidates based on criteria.

"What the British people voted for on the 23rd of June was to bring some control into the movement of people from the European Union to the UK," she told reporters on Monday after a two-day summit of leaders from G20 nations in China. "A points-based system does not give you that control."

May recalled how staff at Heathrow airport had told her that migrants were able to abuse student visa rules when they applied to come to Britain.

"But because they met the criteria they were automatically let in. That's the problem with a points-based system. I want a system where the government is able to decide who comes into the country. I think that's what the British people want."

(Reporting by William James; writing by Kate Holton; editing by William Schomberg)