The British government has won final approval from parliament for legislation giving Prime Minister Theresa May the power to trigger the country's exit from the European Union.

British Brexit minister David Davis welcomed parliament's approval on Monday.

"Parliament has today backed the government in its determination to get on with the job of leaving the EU ... We are now on the threshold of the most important negotiation for our country in a generation," Davis said in a statement.

"So we will trigger Article 50 by the end of this month as planned and deliver an outcome that works in the interests of the whole of the UK."

After members of the lower house of parliament voted earlier in the day to throw out changes to the bill made by the upper house in recent weeks, the upper house also agreed to pass the legislation unamended.

The bill goes next to Queen Elizabeth for final signoff, and May can then invoke Article 50, the formal mechanism for leaving the EU, at any time she chooses.

OPINION: If Scotland leaves, England will lose the Brexit game

Meanwhile, Scotland's leader said on Monday she would seek authority for a new independence referendum because Britain is dragging Scotland out of the EU against its will.

Scottish First Minister Nicola Sturgeon demanded an independence referendum to be held in late 2018 or early 2019, once the terms of Brexit have become clearer.

But May is preparing to reject the demand, The Times newspaper reported.

"The prime minister has said this would mean a vote while she was negotiating Brexit and I think that can be taken pretty clearly as a message that this timing is completely unacceptable," The Times quoted an unidentified British government source as saying.

The results of the June 23 Brexit referendum called the future of the UK into question because England and Wales voted to leave the EU but Scotland and Northern Ireland voted to stay, with an overall 55 percent in favour of leaving.

Scots rejected independence by 55-45 percent in a referendum in September 2014.