Jeremy Corbyn delivers a speech at the Labour Party Conference in 2017 | Daniel Leal-Olivas/AFP via Getty Images Labour members reject leadership on second Brexit vote: poll Party grassroots against Jeremy Corbyn’s position of no second public vote on the Brexit deal.

Eight out of 10 Labour members oppose the party leadership's opposition to a second referendum on an eventual Brexit deal, according to a poll of over 4,000 members of the U.K.'s major political parties.

The survey by the Mile End Institute at Queen Mary University in London, published Thursday, found that 78 percent of the Labour grassroots either agree or strongly agree with having a second vote — something Labour leader Jeremy Corbyn has ruled out.

Support for such a step among the groups of Liberal Democrat and Scottish National Party (SNP) members is even stronger. Among the pro-EU Lib Dem grassroots, 91 percent want a second say on the country's EU departure, along with 87 percent of SNP members questioned.

Just 14 percent of British Prime Minister Theresa May's Conservatives think there should be a public vote on the final deal.

On membership of the EU's customs union, 95 percent of Lib Dem members, 91 percent of SNP members and 85 percent of Labour members wish to remain within it, while the equivalent figures for the EU single market are 96 percent, 95 percent and 87 percent. Just 27 percent of Tory members want to stay in the customs union and 25 percent wish to stay in the single market — reflecting the government's policy of leaving both after Brexit.

Tory members also adopted a harder line on immigration with 83 percent agreeing that all EU member countries' nationals should be subject to the same immigration rules as non-EU nationals. Among Labour, 33 percent agreed with that proposition.

The poll by the Mile End Institute at London's Queen Mary University was carried out among party members of the Conservatives, Labour, Liberal Democrats as well as SNP in June 2017. In total, researchers surveyed 4,117 members of the four parties.