LONDON - Britain wants to make incremental steps on trade with the United States and still believes a bigger free trade deal can be done, Prime Minister Boris Johnson said on Wednesday, despite little public encouragement from U.S. President Joe Biden.

Johnson's government once touted a trade deal with the United States as one of the big prizes of Brexit, but those hopes have dramatically faded after Biden replaced Donald Trump and pushed all trade negotiations down his list of priorities.

Johnson's first visit to the White House this week elicited only a cool response from Biden on trade, prompting headlines in Britain that any chance of a deal had diminished at the meeting.

Asked about that interpretation on Wednesday, Johnson said he disagreed: "There is every prospect of a free trade deal with the United States."

However he went on to describe the strategy as focused on taking smaller steps to improve trade relations, citing what he said was an imminent lifting of a U.S. ban on British lamb imports and previously announced progress to ease trade rows.

"What we're wanting to do is make solid incremental steps on trade," he said.

"The Biden administration is not doing free trade deals around the world right now but I've got absolutely every confidence that a great deal is there to be done."

(Reporting by Kate Holton and William James, Editing by Kylie MacLellan) ((william.james@thomsonreuters.com; +44 207 542 3374; Reuters Messaging: william.james.thomsonreuters.com@reuters.net))