An Australian-style visa system will fail to curb immigration levels in the UK because it is open to abuse, Theresa May has suggested. The Conservative leader said the British electorate called for the end of free movement of people from the EU to the UK by voting Leave at the EU referendum.

But May, a former Home Secretary, argued a points based system – as endorsed by the Vote Leave campaign and Foreign Secretary Boris Johnson – would fail to "give that control".

The prime minister, speaking at the G20 summit in China, said: "Yes, the voters' message on the 23 June was clearly that they didn't want to see free movement continuing as it had done up until now, they wanted to some control in movement of people from the European Union into the UK.

"But we also want to get the best deal possible for trade in goods a services with the EU. I intend to go out there and be ambitious."

May highlighted a visit she took with David Cameron to Heathrow Airport during her time at the top of the Home Office. "We talked to border force officers there and we said to them 'what's the most important thing that we can focus on?'" the prime minister said.

"They said 'well, you need to look at the issue of students, who come here, who appear to have met the criteria, they don't speak English, they don't know which institution they're going to and they don't know what course it is they are doing. So the system is being abused."

Elsewhere, the top Conservative stressed that it remains a "golden era" relations between China and the UK, despite her decision to delay giving the go-ahead to the Beijing backed Hinkley Point nuclear station project.

Back in Westminster, MPs are preparing to debate a second EU referendum after more than 4m people signed an online petition. However, the document was tabled before the result of the historic ballot, centres on voter turnout thresholds and Westminster Hall debates cannot change law.

May, meanwhile, has ruled out holding a second vote on the issue and said she will not trigger Article 50 of the Lisbon Treaty – the official mechanism to split from the EU – this year.