The Home Secretary told the Conservative Party conference there would never be space to house all those who want to come here even if the entire country was concreted over to build more houses, schools and hospitals.
Mrs Braverman said: "The wind of change that carried my own parents across the globe in the 20th century was a mere gust compared to the hurricane that is coming.
"Because today, the option of moving from a poorer country to a richer one is not just a dream for billions of people. It's an entirely realistic prospect."
She said: "Nobody can deny that there are far, far more people in poorer countries who would love to move to Britain than could ever be accommodated.
"Even if we concreted over the countryside, turned our cities into one vast building site and erected skyscrapers from Eastbourne to Elgin and from Hull to Holyhead it still wouldn't be enough.
"Demand will always outstrip supply. I know it. You know it."
In a speech that led to a long standing ovation, the Home Secretary also branded the Human Rights Act the "Criminal Rights Act" she claimed it is preventing the Government from ending illegal migration.
She said the laws, introduced by Tony Blair's Labour government, have "turbocharged" legal challenges. Politicians have been "too unwilling" to recognise that treaties such as the European Convention on Human Rights and the Refugee Convention need updating, Mrs Braverman said.
She added: "The biggest reason why Conservative governments have struggled to get illegal migration under control is because Labour governments passed laws that inhibit effective action. We struggle to remove foreign criminals. We struggle to get accurate data on the ages of those who claim asylum.
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