Theresa May has insisted the government must aim high in the next phase of EU negotiations, during a meeting of her “Brexit war cabinet” that highlighted some divides between senior ministers.

A source revealed that the prime minister argued strongly for the UK to maintain its calls for a “bespoke and ambitious” trade deal despite a suggestion from the EU’s lead negotiator, Michel Barnier, that such an option was not viable.

They said May argued that the UK ought to be thinking less about conforming to European standards and more to international ones as it enters discussions about the future trading relationship.

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.

On Monday a senior adviser to Barnier said the EU could never see Brexit as a success , arguing that it would ultimately weaken both sides economically.

Speaking in London, Stefaan De Rynck also said the UK would have to accept all existing and new EU rules during a transition period, with no possibility of “cherry picking or what one could call a buffet-style transition, where one picks and chooses the bits one likes.”

Those familiar with May’s cabinet session said the focus was not on transition but the ambitions for a trading arrangement in the Brexit “end state”.

They said the 10 key figures, including the chancellor, Philip Hammond, the home secretary, Amber Rudd, and the Brexiters Boris Johnson and Michael Gove were largely united about the broad aim of talks.

They all believe the UK should start by pushing for a bespoke trade deal under which Britain would have the benefits of a Canada-style free trade agreement but with the addition of elements particularly important to the UK, such as services.

Beyond that they divided into “divergers” and “aligners”, according to the source, with Rudd and Hammond falling into the latter category and arguing that continued closeness to EU regulations was critical for the economy.

There was a fair amount of discussion about the importance of jobs in the future, but the home secretary stressed the importance of existing employment and argued that alignment with European standards would help protect that, they revealed.

Meanwhile, Johnson and Gove – along with Liam Fox and the defence secretary, Gavin Williamson, think long-term benefits can be gained by moving further away from a European-style economy and making it easier to sign up to deals with third countries.

One source said the balance in the room tipped to those backing more alignment with the EU, but said the position of the prime minister was still unclear.

The Brexiters will be heartened by hearing May argue about global standards, a position that is also held by key figures in her Brexit negotiating team. However, critics have said the EU is one of the major torchbearers for global standards.

The group have not yet discussed their hopes for a transition period, but some of their views could leave Britain at loggerheads with the EU over an implementation process.

Gove wants Britain to leave the common agricultural and fisheries policy during transition, not least because the country will no longer have a place at the table during that period. That would mean in fisheries, for example, that the UK would have no say in quota levels but would have to abide by them.

A Downing Street source said the issues would be placed in the “negotiating bucket” but argued that the prime minister wanted things to remain broadly the same for that period.

During his session, De Rynck argued that the UK would have to accept the rules but could not influence the EU during transition because it would have left the bloc by then.

“There is some reluctance on these conditions, but I should stress that these conditions are in the interests of the UK and EU economies alike,” he said.

“Because part of the reason to have a transition is that business wants to adapt only once to a new regime. Not just business – UK customs authorities and EU customs points will need to adapt to a new regime once the future relationship starts. And so transition with uncertainty in the rules seems to me in no one’s interest.”