More than 16,000 people have emailed Labour over the past five days, urging the party to consult members on Brexit after MPs said the topic was being ignored by its most senior policy body.

The emails from party members will be examined by the party’s national policy forum (NPF), which meets this weekend in Leeds, and whose members include the shadow cabinet and trade union leaders.

Labour has set up eight policy commissions since last year’s general election, to consult members and develop policy, but none focus on Brexit. The party has said Brexit is covered under the international policy commission, involving Keir Starmer, the shadow Brexit secretary, but that commission is not at the moment accepting submissions on Brexit. A leaked draft of the commission’s agenda for the meeting this weekend, seen by the Guardian, shows members will be asked for views on development goals, not on Brexit.

Questions to the forum include “how can Labour best make the argument for international development?” and “what would a world for the many, not the few, look like in 2030, and how could Labour’s international development policy contribute to achieving it?”

The economic, business and trade commission, attended by Barry Gardiner, the shadow international trade secretary, also makes no mention of Brexit in a description of its work.

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.

The NPF has set aside an hour-long discussion on Brexit at this weekend’s meeting but MPs have been pushing for the party to commit to setting up a separate forum.

The email campaign, which led to 16,548 emails being sent to the party on the subject, follows a letter from more than 30 Labour MPs, MEPs and activists last Thursday to the party’s national executive committee, which set up the policy forums.

MPs who have highlighted the issue, including Heidi Alexander and Alison McGovern, believe that giving members a forum to have their say on the party’s Brexit policy will reveal how many of those people favour remaining in the single market and customs union.

The campaign for members to have more say follows controversy at last year’s Labour party conference when Momentum’s powerful caucus effectively blocked a vote on making single market membership Labour’s policy. The result could have been potentially embarrassing for Jeremy Corbyn, the Labour leader, as it may have put party members, the majority of whom are pro-remain, at odds with Labour’s official policy to leave the single market.

Momentum advised its members to vote for other topics, however, successfully keeping the issue off the table during the eight motions selected for a conference vote.

The party has been more ambiguous on the customs union, with Corbyn and Starmer suggesting they are open to the UK remaining a member.

Corbyn has been a longtime champion of a greater role for members in decision-making, as has Jon Lansman, a member of Labour’s NEC and the founder of Momentum.

The Labour leader, who has been sceptical of EU membership in the past but campaigned for a remain vote, has kept the party’s Brexit policy relatively vague, but said Labour was seeking a “jobs first” exit deal.

Alexander, who co-chairs the group Labour for the Single Market, which is backed by pro-single market campaign group Open Britain, said the party could not continue to brush the issue under the carpet.

She said: “Without this, it is genuinely not clear how Labour members, supporters and the public are meant to contribute to the party’s policymaking on the biggest issue we face as a country. Local Labour branches all over the country have been debating this issue for a year and a half, and yet when it came to party conference in September the motions they had passed and the views they expressed were effectively junked.”

McGovern, who co-chairs the group with Alexander, said Labour should not “bury its head in the sand” and should present a coherent vision of a post-Brexit future. “Now is the time for the Labour party to reject this extreme Tory Brexit and instead chart a progressive path forward.”

Labour has said the policy issues would be considered through the eight policy commissions. “The commission and wider NPF are looking at Brexit this year in meetings, evidence sessions and by considering all submissions received,” a spokesman said. “There is a Brexit discussion at the meeting this weekend and each of the eight commissions has its own dedicated Brexit representative to ensure work is coordinated across the whole NPF.”

On Thursday, Richard Angell, the director of Labour’s centrist pressure group Progress, wrote an editorial arguing that policy of remaining in the single market would be the best move by Corbyn to unite all Labour members across the political spectrum as well as in leading trade unions.

In a piece for Progress magazine, Angell said single market membership “unites all in the Labour party but the smallest Bennite tendency in the shadow cabinet and leader’s office”. He wrote: “The only option for an anti-austerity party is to stay in the single market and customs union. The Labour membership already knows it, but the Labour leadership has yet to come to the same conclusion. It must, soon.”