The international trade secretary, Liam Fox, has said a post-Brexit trade arrangement with the US may take longer to agree than some people hope, after reports that Boris Johnson would make this a priority if he becomes prime minister.

Fox said potential complications could include different rules across American states and the start of the presidential electoral cycle. He also stressed that no deal could be agreed before the UK formally left the EU.

Fox told BBC Radio 4’s Today programme there had already been six meetings of a trade working group with the US to examine the issues.

“One of the things you have to remember about the US is that not all trade policy is actually done at the federal government level,” he said. “A great deal of the trade policy is done at the state level, particularly in the non-tariff barriers to trade, things like regulation. We have been increasing the number of our staff in the US who are expert at the state-to-state level.”

On Monday the Times cited unnamed “allies” of Johnson as saying he hoped to have a simple trade pact with the US, possibly on one area of trade, ready to go on the day of Brexit, due on 31 October.

Fox reiterated that a deal could not be agreed before then, saying: “We can’t negotiate anything with the US until after we’ve left the European Union. It would be in breach of European law for us to do that.”

He said even a seemingly straightforward, single-element initial deal could be held up. “You have got the added complication that we’re now getting very close to the American pre-election year, where it’s quite hard to get things through Congress. So even if you negotiate them quickly you wouldn’t necessarily get to ratify them.”

Fox also said trying to separate talks on food and agriculture, given UK consumer worries on US standards, could prove tricky. “If you go to the US and you say we’re going to take any discussions on agricultural access off the agenda, you will find that they close down pretty quickly in terms of the willingness to discuss things.”

He added: “But it’s certainly true that we should be trying to get an agreement with the United States as quickly as we possibly can.”

On the issue of who should succeed Sir Kim Darroch, the UK ambassador in Washington, who announced last week he was stepping down after criticism from Donald Trump in the wake of the leak of UK diplomatic cables, Fox said he would be happy for it to not necessarily be a career diplomat.

“I’ve always thought that we should be using a wider range of people in some of our diplomatic posts,” Fox said, citing “senior politicians” as one possibility.

On a warning to newspapers by the Metropolitan police about printing more leaked missives, Fox said he backed the rights of a free press but that editors should stay within the law. “Newspapers have to be very clear about their responsibilities, which is to remain within the law,” he said.

Asked about publishing such leaks, he said: “They will have to make their own decisions on that. It’s quite right that the press will publish what they believe will be of political interest, but of course it’s not acceptable to stray over the line into breaking the law.”

On whether the Mail on Sunday should have published the leaks that led to Darroch’s resignation, Fox said: “That’s not for me to say.” He added: “We have to have a free press. They have to feel they are able to say what they want to say. They need to respond to public concerns. What they cannot do, of course, is stray over the line of legality.”