Mrs May was addressing Conservative members at the party’s annual conference, in a speech seen as vital for her prospects of remaining Prime Minister as rows over Brexit continue.
The Prime Minister took aim at First Minister Nicola Sturgeon, who wants to delay Brexit, over her approach to fishing after the UK leaves the European Union.
Ms Sturgeon has been accused of politicians in Scotland, as well as some industry leaders, of seeking to leave control of Scotland’s fishing waters with Brussels indefinitely.
Mrs May said: “Let me say this to Nicola Sturgeon: you claim to stand up for Scotland, but you want to lock Scottish fishermen into the Common Fisheries Policy for ever.
“That’s not ‘stronger for Scotland’. It’s a betrayal of Scotland.”