Theresa May set out her vision for the UK’s post-Brexit relationship with the EU in a speech next Friday, No 10 has announced, after she and senior cabinet members spent Thursday at Chequers hammering out a position.

In a sign that the prime minister’s agreed position is expected to face resistance from Brussels, Downing Street reiterated her aim that EU nationals entering the UK during a transition period would have fewer rights than those already in the country.

The EU considers this unacceptable, with Guy Verhofstadt, the European parliament’s Brexit coordinator, saying at the weekend that May was “not very serious” when she proposed this.

One senior Brexiter emerged from the eight hours of cabinet talks at Chequers, the PM’s official country retreat in Buckinghamshire, to say “divergence was the victor”. However, May’s spokesman gave few details on what had been decided.

“It was a very positive meeting and a step forward, agreeing the basis of the prime minister’s speech on the future relationship,” he said. “Discussions will now take place at cabinet and you expect the prime minister to deliver her speech next Friday.”

The speech is expected to be delivered in the UK but the location is yet to be revealed.

Speaking earlier, Jeremy Hunt, the health secretary, confirmed the government would not consider entering into a customs union with the EU after Brexit, setting up a potential Commons battle with Tory rebels and Labour.

Leading pro-remain MPs from both parties tabled an amendment on Friday to the government’s trade bill calling for continued participation in a customs union – and said there was enough Commons support for it to pass.

Asked whether the government would consider thinking again on the issue, Hunt told BBC Radio 4’s Today programme: “No. Because, if we were part of the customs union, we wouldn’t be able to negotiate trade deals independently with other countries and we wouldn’t have full sovereign control of our destiny as a nation.”

Quick Guide What are Brexit options now? Four scenarios Show Staying in the single market and customs union The UK could sign up to all the EU’s rules and regulations, staying in the single market – which provides free movement of goods, services and people – and the customs union, in which EU members agree tariffs on external states. Freedom of movement would continue and the UK would keep paying into the Brussels pot. We would continue to have unfettered access to EU trade, but the pledge to “take back control” of laws, borders and money would not have been fulfilled. This is an unlikely outcome and one that may be possible only by reversing the Brexit decision, after a second referendum or election. The Norway model Britain could follow Norway, which is in the single market, is subject to freedom of movement rules and pays a fee to Brussels – but is outside the customs union. That combination would tie Britain to EU regulations but allow it to sign trade deals of its own. A “Norway-minus” deal is more likely. That would see the UK leave the single market and customs union and end free movement of people. But Britain would align its rules and regulations with Brussels, hoping this would allow a greater degree of market access. The UK would still be subject to EU rules. The Canada deal A comprehensive trade deal like the one handed to Canada would help British traders, as it would lower or eliminate tariffs. But there would be little on offer for the UK services industry. It is a bad outcome for financial services. Such a deal would leave Britain free to diverge from EU rules and regulations but that in turn would lead to border checks and the rise of other “non-tariff barriers” to trade. It would leave Britain free to forge new trade deals with other nations. Many in Brussels see this as a likely outcome, based on Theresa May’s direction so far. No deal Britain leaves with no trade deal, meaning that all trade is governed by World Trade Organization rules. Tariffs would be high, queues at the border long and the Irish border issue severe. In the short term, British aircraft might be unable to fly to some European destinations. The UK would quickly need to establish bilateral agreements to deal with the consequences, but the country would be free to take whatever future direction it wishes. It may need to deregulate to attract international business – a very different future and a lot of disruption.

Speaking on the same programme, the pro-remain Labour MP Chuka Umunna warned the government it would have to change its position or face losing a key Commons vote, which would be seen as a direct challenge to May’s authority.

He said the “reality of the parliamentary arithmetic” was that there was no majority in favour of the government’s position. “And, if they are not going to change their position, they’re going to lose votes in the House of Commons. It’s as straightforward as that,” he said.

Asked what May’s message would be to Tory MPs thinking about backing the amendment, her spokesman said: “The message is that we are working towards securing a deal which will deliver as frictionless trade as possible, and will be a good deal for all parts of the United Kingdom, and we believe that that is a deal that everyone should be able to support.”

And he was adamant there would be no movement over the rights of EU citizens during a transition period after March 2019, dismissing reports on Friday of a possible U-turn on the issue.

He said: “In terms of people who are arriving after March 2019, they arrive under a different set of circumstances to those who arrived before, with different expectations, and you can expect their rights to reflect that. Their rights will be different.”

I understand many others will add their names today. https://t.co/Z5POSKWT7C — Anna Soubry MP (@Anna_Soubry) February 23, 2018

BREAKING: the @eurelationsappg new cross party clause 5 to the Trade Bill just tabled by @Anna_Soubry,me, @NickyMorgan01, @S_Hammond & others providing for the UK to continue participating in a Customs Union with the EU -I believe we have a majority in the House of Commons for it pic.twitter.com/IfdpsXt2Yi — Chuka Umunna (@ChukaUmunna) February 23, 2018

While Labour’s official position on the amendment has not yet been made clear, it emerged on Thursday evening that Jeremy Corbyn was likely to announce the party’s backing at a key Brexit speech on Monday.

The party was known to view customs union membership as “viable”, but there were indications from some senior shadow cabinet members that Labour was ready to formalise its support for it.

John McDonnell, the shadow chancellor, said on Thursday that Labour’s position was “evolving”, which Umunna interpreted as an indication of support for the amendment.

On Friday, Hunt, who did not attend the Chequers talks but will be at the full cabinet meeting to discuss the plans later, – said the government wanted “frictionless trade” with the EU, but added that he recognised ministers would need to “find a different way” to do it.

“Customs union is one way of getting frictionless trade, but it’s not the only way and what we’re saying is that we want to achieve frictionless trade by agreement between two sovereign bodies: the United Kingdom and the European Union,” Hunt said.