She added: “What the British people voted for on the 23rd of June was to bring some control into the movement of people from the European Union to the UK. A points-based system does not give you that control.”
Mrs May’s acknowledgement has concerned former Ukip leader Nigel Farage, who says he is “worried” by her remarks.
Mr Farage said: “The people were clear in wanting a points-based immigration system, which is why so many went out and voted to leave the European Union. Any watering down from that will lead to real anger.”