Philip Hammond wants to see Britain retain access to the single market in specific sectors such as financial services, while also securing border controls for the UK.

The chancellor wants to ensure that Brexit negotiations protect particular parts of the economy before a meeting of the cabinet on Wednesday at Chequers.

Theresa May is expecting her most senior ministers to arrive at the prime minister’s country retreat armed with ideas about how Brexit could be a success in their particular areas, having demanded they draw up plans before the summer.

The meeting will take place after reports of a government split over whether or not the UK government should try to retain its membership of the single market.

According to the Sunday Times, a number of senior figures including Hammond believe that all options, including staying in the single market, should remain on the table even if it means fewer restrictions over immigration. This is believed to be in contrast to Brexit-supporting ministers including David Davis and Liam Fox, who are thought to be more hawkish about Britain’s exit plans.

However, a Treasury source was keen to play down the idea of a split. “Everyone agrees there have to be controls on immigration and some access to the single market – taking a flexible approach,” he said.

It has been suggested that the financial services industry will be a priority for the chancellor.

Other European leaders have suggested the UK cannot keep full membership on economic and trade terms if it wants to restrict freedom of movement, arguing that that is one of the four key principles of the European project.

The issue is likely to cause tension within the cabinet, where most ministers campaigned to remain in the EU, but also more widely across government, with some Brexiters deeply suspicious of the motivations of pro-EU civil servants. Steve Baker MP, who campaigned for Brexit, has suggested that officials should be “summarily fired” if they tried to block the Brexit process.

The question for negotiators will be what access to the market actually means. Some Brexit supporters believe European countries will give the UK tariff-free trade alongside restrictions to immigration but many others expect there to be an economic price to pay for greater border control.

The former head of the civil service, Gus O’Donnell, recently suggested Britain could remain in a more “loosely aligned” European Union, arguing it could take “years and years and years” to separate fully and that the whole project could change in that time. However, he said it was unlikely that any reform would be radical enough, arguing the chances of remaining a part of the European project were very low.

O’Donnell urged caution in triggering article 50 without a strategic plan in place, arguing that the exit mechanism from the EU was designed to favour the countries that were staying in the union.

The process that will take place before a formal UK exit has caused a backlash in parliament after it emerged that May will not give MPs a vote before invoking article 50. Downing Street sources said May was clear that the will of the British public would be honoured, with her repeated assertion that “Brexit means Brexit”.

However, politicians, who campaigned overwhelmingly for Britain to stay in the EU, want to have a say on the deal the UK government secures.

Barry Gardiner, Labour’s shadow secretary of state for international trade, Europe, energy and climate change, said parliament could not be sidelined from the greatest constitutional change the country has debated in 40 years. “The logic of saying the prime minister can trigger article 50 without first setting out to parliament the terms and basis upon which her government seeks to negotiate, indeed without even indicating the red lines she will seek to protect, would be to diminish parliament and assume the arrogant powers of a Tudor monarch,” he said.

Owen Smith, the leadership candidate for Labour who has sought to make the EU a dividing line between him and Jeremy Corbyn, accused the prime minister of “running scared” from parliamentary scrutiny of her Brexit negotiations. “She’s looked at the numbers and she knows she might not win a vote in parliament. She hasn’t set out what Brexit means and she doesn’t want to be held to account on vital issues such as stripping away workers’ rights and environmental safeguards.”

Smith has argued that the Brexit deal should be put to the public vote through a second referendum or a general election but Corbyn has argued that the outcome of June’s vote has to mean Brexit.