Labour has said it expects significant new proposals from the government when senior party figures meet cabinet ministers to resume Brexit talks, including on single market alignment, a customs union and protections against a future Tory leader unpicking any agreement.

The shadow chancellor, John McDonnell, the shadow Brexit secretary, Keir Starmer, the shadow business secretary, Rebecca Long-Bailey, and the shadow environment secretary, Sue Hayman, will lead the talks for Labour. McDonnell, who was joining the talks for the first time, said Labour was engaging seriously but needed to hear new proposals.

On the Tory side the chancellor, Philip Hammond, and the environment secretary, Michael Gove, will join the Cabinet Office secretary, David Lidington, the business secretary, Greg Clark, the Brexit secretary, Steve Barclay, and the chief whip, Julian Smith, for the talks, which are expected to run until 5.30pm, including an informal lunch.

McDonnell said the customs union was the first item on the agenda for the talks, followed by closer alignment with the single market, workers’ rights, consumer and environmental protects and a lock to prevent the agreement from being undone – including potentially striking a binding deal with the EU.

He said a second referendum was also on the agenda, though he expressed scepticism about whether the talks would get to that stage of the agenda within the allotted four-and-a-half hours. “Whether we reach it, we’ll see,” he said.

McDonnell said correspondence had been exchanged between the two sides since Friday but no new proposal had been outlined. “What there hasn’t been sufficient discussion of so far is alignment with the single market,” he said. “So Philip Hammond’s there today and we will be expecting him to outline in more detail the proposals that they have.”

He said Labour remained particularly concerned about protecting any deal from being unpicked by a new prime minister. “On the agenda we’ve maintained the discussion about entrenchment – how do we secure any deal that comes forward in the long term?”

McDonnell said he noted with concern comments by the attorney general, Geoffrey Cox, who said future governments could not be bound forever by agreements. “There’s nothing to stop us removing ourselves from that arrangement, so we can’t look at these things as permanent straitjackets upon this country,” Cox said last week.

McDonnell suggested any deal done with Labour would have to be written into an EU-level text. “We can have greater security as a result of international agreement,” he said. “It’s more than being in written legislation, it’s about the agreement we have with the EU.”

Asked if that meant reopening the binding withdrawal agreement, which the EU has repeatedly declined to do, he said: “It doesn’t necessarily have to be reopened but there has to be some element in which an agreement can be secured in that way. We are asking for a clearer proposal on how we can have that security for the longer term.”

McDonnell said remarkably little progress had been made so far on Labour’s central demand for any future deal to include a permanent customs union. “They are not even giving us any changes in language. But we will see what comes out of today,” he said.

Hours before the talks were due to resume, Liam Fox, the international trade secretary, wrote to Conservative MPs saying a customs union would be the “worst of both worlds”. His comments suggest he would be unable to remain in the cabinet if May were to agree to a customs union.