By Kylie MacLellan

LONDON (Reuters) - The British government will set out in the coming week how it plans to shape its relationship with the European Union upon leaving the bloc, Prime Minister Theresa May said in an interview broadcast on Sunday.

Since taking office in July, May and her Brexit minister David Davis have given little detail about what Britain's future relationship with the EU will look like, saying only they want it to involve curbs on immigration and a good deal on trade.

"He (Davis) will be making a statement to parliament this week about the work that the government has been doing over the summer and obviously how we are going to take that forward in shaping the sort of relationship we want with the EU," May told the BBC in an interview recorded before she left Britain for the G20 summit in China.

On her way to the summit, May told reporters Britain's economy will suffer as a result of the decision to leave the EU despite signs in recent economic data that the impact has not been as severe as some predicted.

May told the BBC she would use the summit to begin talks with world leaders including U.S. President Barack Obama, Indian Prime Minister Narendra Modi and Australian Prime Minister Malcolm Turnbull over future trade deals.

"I want to talk about how we can scope out what a trade deal and the negotiations on a trade deal would be like so that when the time comes, when we are able to sign those deals, we are able to do so," she said.

May, who upset Chinese officials by delaying a $24 billion project to build a partly Chinese-funded nuclear power plant, is also due to hold a one-to-one with Chinese President Xi Jinping at the summit. She told the BBC she would be making a decision on the deal later this month.

May has been clear she will not trigger Article 50, the formal process of leaving the EU, this year in order to give Britain time to prepare for upcoming negotiations, but said it would not be "kicked into the long grass".

May said there would be no early national election, despite some in her ruling Conservatives believing turmoil in the opposition Labour Party gives them an opportunity to increase their small parliamentary majority.

"We need that period of time, that stability to be able to deal with the issues that the country is facing and have that election in 2020," she said.

She also dismissed comments by Scottish First Minister Nicola Sturgeon that the Brexit vote had shifted the debate on Scottish independence just two years after Scots voted by 10 percentage points to reject it. Opinions polls did not suggest the Scottish people want another vote, May said.

(Editing by Raissa Kasolowsky)