LONDON (Reuters) - Andrea Leadsom, one of three candidates vying to be Britain's next prime minister, said on Thursday she would guarantee that all immigrants living legally in Britain would be welcome to stay after the country exits the European Union.

Leadsom, a junior energy minister who before going into politics had a long career in the financial services industry, said that after Brexit those who wanted to travel and study in Europe would be free to do so.

"We have to give certainty to different groups in our own country. Certainty on migration. We want fair but controlled immigration, fair to those who are already here and fair to all the talents across the world," Leadsom said in a speech.

"People need certainty and they will get it. I say to all who are legally here that you will be welcome to stay."

(Reporting by Estelle Shirbon, Kate Holton and William James; editing by Costas Pitas)