The Green party now has more members than Ukip and the Liberal Democrats after gaining more than 2,000 supporters in the last day alone.

The surge in support coincides with a blaze of publicity for the Greens over their exclusion from the proposed televised leaders’ debates because they are not considered a major party. The criteria for being classed as major does not include membership but is based on a party’s standing in opinion polls and success in elections.

However, supporters have been rushing to sign up all the same, meaning the Greens now have 44,713 members across their three UK parties – just ahead of the Lib Dems. This makes them the fourth biggest UK-wide party in terms of membership, although the Scottish National party has a much bigger base of around 92,000.

Ukip has seen a rise in membership over the last year and now has 41,943 signed-up supporters, while the Liberal Democrats’ last published total was 44,576.

The Green party said its ongoing membership growth and latest polling further called into question Ofcom’s initial view that it was not a major party. Some opinions polls suggest the Greens are ahead of the Lib Dems in terms of voter support.

The party’s leader, Natalie Bennett, said: “This second significant advance in a day reinforces the Green party’s case to be included in the broadcasters’ proposed leaders’ debates.

“At the May 2014 European elections we saw three Green MEPs elected to the Lib Dems’ one, we are polling level or above them with several pollsters, and now we have more members than them.

“I offer my thanks to everyone who has joined us and help send a message to the broadcasters and the regulator, Ofcom, that the Greens’ anti-austerity message – that we have to stop making the poor, the disadvantaged and the young pay for the errors of the bankers – must be heard.”

Bennett has written to the leaders of Labour, Ukip and the Liberal Democrats urging them to ask the broadcasters to include the Greens in the debates.

David Cameron has said he will not participate in the debates if the Green party is excluded, claiming that it would be unfair to leave them out if Ukip and the Liberal Democrats take part.

However, Ed Miliband, the Labour leader, said the prime minister’s argument about the Greens was a “pathetic excuse” made up so that he did not have to debate with Labour and Ukip.