5.01pm: May is still speaking.
She says courts have had to decide whether people can use their right to a family life under article 8 of the European convention on human rights to stay in the UK on the basis of case law.
But parliament should have a say, she says.
She will soon ask the Commons to approve a motion setting out new immigration rules. These will make it clear that article 8 rights are qualified, she says.
4.56pm: Theresa May says the governement has already reformed other aspects of the immigration system. Now it is turning to family migration.
Ministers want to get annual migration down below 100,000, she says.
Family migration accounts for 18% of immigration, she says.
Three conditions should apply to family migration: marriages should be genuine, people should be able to pay their way and migrants should be able to integrate, she says.
For too long the immigration system did not take into account whether people coming to the UK would be able to pay their way.
In future there will be a threshold, set at £18,600 for a partner. The threshold will be higher if they have children.
A threshold will also apply if people want to bring in relatives who require care.
4.55pm: Theresa May, the home secretary, is making her statement on family migration.
