Mrs. May’s government, Ms. Sturgeon said, did not give advance notice to leaders of Scotland, Northern Ireland and Wales, the other components of the United Kingdom, when the British leader decided that March 29 was the day she would invoke the Article 50 clause of the European Union treaty, starting the withdrawal from Europe, known as Brexit.

“If I told you that not just the Scottish government, but the Welsh government and Northern Ireland found out the date of the triggering of Article 50 from the BBC, it probably gives you an insight,” Ms. Sturgeon said.

Representatives of Mrs. May’s government did not immediately respond to email requests for comment. But Mrs. May, the top advocate of Brexit, has said that she believes all constituents of the United Kingdom should now grow more unified, and that she strongly opposes Ms. Sturgeon’s push for Scottish independence.

“Now is not the time,” Mrs. May said last month in public remarks that seemed to Ms. Sturgeon and her supporters patronizing and arrogant.

Ms. Sturgeon, 46, leader of the Scottish National Party, has emerged as a formidable force in the independence effort, which failed in a 2014 referendum but found renewed energy after the Brexit referendum in June produced a victory for those who wished to leave the European Union.