Tony Abbott, the former Australian prime minister, has declared that Europe is facing a "peaceful invasion of would-be economic migrants" from the Middle East and Africa. Abbott said the prospects of millions of people "streaming into Britain" had "pushed the Brexit vote over the line."

In an uncompromising speech to centre-right members of the European parliament on 17 September, Abbott said uncontrolled migration had not caused Brexit – but "had prompted Britons to take back their sovereignty."

Abbott said that too many migrants were coming to Europe "with a grievance" and a feeling that "Europe should make way for them".

"Of course, it is a decent and a humane impulse to give a better life to people from wretched places. But once people have gone beyond their first place of safety, they're not asylum seekers but would-be economic migrants.

"For some years, 500 million Europeans probably could absorb current inflows provided the newcomers were joining in, rather than breaking in. But a million people coming by boat and almost a million people coming by land last year has the look of a peaceful invasion.

"Many of those taking to boats across the Mediterranean or clamouring at Europe's gates look set to join an angry underclass. Turkey's President, in an exuberant moment, has urged Muslims to take back parts of Europe; and among the would-be migrants are soldiers of the caliphate bent on mayhem.

"Too many are coming, not with gratitude but with grievance, and with the insistence that Europe should make way for them."

Abbott used his speech in Prague to the Alliance of European Conservatives and Reformists – an umbrella group of 30 centre-right European parties – to argue that Australia's tough policy of border protection had worked.

Australia has maintained strict border controls in keeping out unwanted migrants but it has faced criticism for using off-shore detention centres to house migrants. Abbott has said these policies have actually saved the lives of people as they dissuade migrants from making perilous sea crossings to Australia.

Leave campaigners during the EU referendum campaign pointed to Australia's tough immigration policies – such as its points system – as a blueprint for the UK.

"This crisis can't be managed; it has to be resolved," Abbott told the gathering of lawmakers. "That's what Australia did, under my government: we stopped illegal boats at sea and escorted them back to Indonesian waters.

"If the boats were scuttled, we had big orange life rafts on hand so that people could safely return from whence they'd come. I knew the risks to our personnel; I knew the damage this would do to relations with Indonesia; I knew the outcry it would spark from well-meaning activists but it simply had to be done.

"Effective border protection is not for the squeamish, but it is absolutely necessary to save lives and to preserve nations. The truly compassionate thing to do is: stop the boats and stop the deaths – and, for more than two years now, there have been no illegal arrivals by boat in Australia and the drownings have stopped."

Abbott, who was prime minister for two years until September 2015, said it was the responsibility of conservatives not to resist populism but to engage with people's concerns. He remains a member of the Australian parliament.

"Disapproval of Brussels' handling of the migration crisis runs as high as 94% of Greeks, 88% of Swedes and 77% of Italians," Abbott said. "Acknowledging people's concerns about uncontrolled immigration should help to build trust on other changes, especially the economic ones, that have to be accommodated."