LONDON—President Trump’s national security adviser said he told British Prime Minister Boris Johnson the administration would strongly support the U.K.’s exit from the European Union in late October—deal or no deal.

John Bolton was the highest level U.S. official to meet with Mr. Johnson during a visit Monday to London. Mr. Bolton held meetings with the country’s new government looking to kick-start trade and defense talks and convey the administration’s support amid uncertainty about what Britain’s exit from the EU would look like.

Mr. Bolton told reporters that if Mr. Johnson decided to exit from the EU without a deal on Oct. 31, “We are supporting that enthusiastically.” He said he told British officials: “That’s what I’m trying to convey. We’re with you, we’re with you.”

Mr. Johnson’s rising threats to take Britain out of the EU with or without a deal by the Oct. 31 deadline have increased the once-remote prospect of a no-deal Brexit. Officials on both sides have revived planning aimed at reducing disruption ranging from information campaigns, planning of emergency transport for essentials like medicines to accelerated hiring of customs officers.

A spokesperson for Mr. Johnson said he joined a meeting at Downing Street between senior officials and Mr. Bolton, in which they discussed “the close U.K.-U.S. trading relationship and our shared commitment to an ambitious free-trade agreement once the U.K. leaves the EU.”