Labour has been accused of attempting to kick Brexit into the “long grass” after Keir Starmer revealed that he planned to pile pressure on the government to keep Britain inside the single market during a transitional period.

The shadow Brexit secretary made clear that he could exploit Theresa May’s lack of majority by working cross party to secure a closer economic relationship to the EU for up to three years after the formal exit.

He told the Guardian he would table amendments to the EU withdrawal bill to ensure it was “possible to achieve transitional arrangements on the same basic terms – including the single market and the customs union”.

Starmer said the bill in its current form was not acceptable, partly because it “dismantles the apparatus of the single market and the customs union and it extinguishes any role for the European court of justice”.

Tory MPs and advisers hit back at the suggestion, accusing Labour of playing games in an attempt to delay Brexit indefinitely.

Charlie Elphicke, MP for Dover, said: “There is a clear instruction from the British people to end uncontrolled EU immigration and that means leaving the single market in March 2019.”

He argued that Labour had made clear in its election manifesto that it would end free movement but could only do so by leaving the economic grouping.

“It would be wrong for the Labour party to seek to undermine the referendum decision or seek to kick it into the long grass,” said Elphicke.

A senior Tory source agreed, claiming everyone knew the “four pillars” of the single market, including free movement were indivisible.

“Labour don’t know what they are doing. You’ve got [Jeremy] Corbyn confirming we are leaving the single market and senior members of the shadow cabinet saying we should take nothing off the table.

“They’ve got a GCSE-level understanding of Brexit and that is totally inconsistent and letting down Labour members and the country as a whole.”

The four pillars of the single market are free movement of goods, persons, services and capital between members states.

The Conservatives are hoping to hit back at Labour by exploiting potential differences at the top of the party after the shadow trade secretary, Barry Gardiner, wrote in the Guardian that Brexit meant leaving the single market and customs union.

That assertion angered Starmer, who went on to contradict his colleague in subsequent days.

The question of transition has been raised since the chancellor, Philip Hammond, said an interim Brexit deal would be necessary. Although he said that Britain must leave the single market in the spring of 2019, Hammond has also privately said that the UK could seek an “off the shelf” solution and conceded that while free movement would technically end, immigration controls could be delayed.

Labour is facing pressure from both sides because it has a number of constituencies that voted to leave the EU but its membership is overwhelmingly in favour of staying inside the single market and, even, of a second referendum.