Home Secretary Theresa May is set to issue a stern warning against high immigration levels, saying the influx threatens the cohesion of British society. She will tell the Conservative Party conference in Manchester that the scale of immigration faced by the UK in the past decade is unsustainable.

"There are millions of people in poorer countries who would love to live in Britain, and there is a limit to the amount of immigration any country can and should take. While we must fulfil our moral duty to help people in desperate need, we must also have an immigration system that allows us to control who comes to our country," May, considered a potential successor to Prime Minister David Cameron as Conservative party leader, would say at the conference.

She will add: "Their desire for a better life is perfectly understandable, but their circumstances are not nearly the same as those of the people fleeing their homelands in fear of their lives ... When immigration is too high, when the pace of change is too fast, it's impossible to build a cohesive society. It's difficult for schools and hospitals and core infrastructure like housing and transport to cope."

The home secretary is to renew the 2010 pledge to cut net immigration below 100,000. During her five-year tenure, immigration numbers have increased to 330,000 a year.

With the net UK migration figures standing at a record high, May will also announce that Britain would no longer allow European Union nationals to make asylum claims in the country. Revealing that 551 asylum applications have come from EU member states citizens in the last five years – costing £4.2m of taxpayers' money – she will say: "We will end this absurdity, saving public money and creating space in our asylum system to help more people who really need our protection."

May will be addressing the conference amid speculation on who will take the baton from Cameron. Boris Johnson will also address the Tory conference and this will be his last speech as London Mayor. Johnson will tell his party colleagues that welfare reforms should protect the lowest paid workers.