LONDON (Reuters) - British Prime Minister Theresa May rebutted U.S. President Donald Trump’s warning about the future of anglo-American trade, saying a trade deal was possible and that work toward it was making good progress.

Trump said on Monday the agreement by which the United Kingdom will leave the European Union may make trade between Washington and London more difficult - handing ammunition to May’s critics at home who want to block the Brexit deal.

She said on Tuesday: “We will have an independent trade policy and we will be able to do trade deals with countries around the rest of the world,” citing a political declaration on future relations with the EU agreed in Brussels on Sunday.

“As regards the United States, we’ve already been talking to them about the sort of agreement that we could have in the future,” she told broadcasters. “We’ve got a working group set up which is working very well and has met many times.”

May’s spokesman said there had already been positive and productive discussions on an ambitious trade deal through joint working groups and cited public consultations on both sides of the Atlantic as signs of progress.

Asked whether May planned to hold a bilateral meeting with Trump at a G20 summit later this week, the spokesman said there were no such plans.

“It’s not something we’ve requested,” he said. “We’ve met with the president on a number of occasions in recent months.”

With May facing a difficult battle to get parliament to approve her deal, Trump’s words struck at the heart of the government’s key argument for the current Brexit accord: that it would allow Britain to strike new global trade deals without abruptly shutting off access to EU markets.

Alongside the prime minister’s words, the government published a “press rebuttal” blog expanding on her arguments and setting out Britain’s plans to pursue a range of post-Brexit trade deals and play an active role on the world stage.

“After we leave the EU in March next year, we will take up our independent seat at the (World Trade Organization) where we will play an active role in negotiations and be strong advocates for the rules-based global trading system,” the blog said.