The Greens are now within a whisker of overtaking Ukip and the Liberal Democrats to become the third biggest UK-wide political party in terms of membership, after a huge surge in support after their exclusion from the television debates.

The party now has 41,567 members, which is just a few hundred behind Ukip’s 41,943 and a few thousand behind the Liberal Democrats’ last total of 44,576. The boost in support for Green leader Natalie Bennett’s party coincides with a burst of publicity about the fact she may not be allowed to take part in the televised election debates because the party is not considered big enough.

On Wednesday night, a Green party official said about 200 members had joined in the previous few hours and there had been a significant intensification of people signing up in the previous 24 hours.

Adam Ramsay, a Green-supporting journalist and election analyst, said membership of the three UK Green parties (including Scotland’s and Northern Ireland’s) would soon exceed that of Ukip and the Liberal Democrats if it carried on growing at the same rate. Writing for OpenDemocracy, he said this could take place as early as next week.

However the Greens still lag behind the SNP, which has 92,187 members but is not a UK-wide party.

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. As it stands, she will probably be excluded if the contest happens as Ofcom, the media regulator, said the Greens do not have enough support to be considered a major party at this stage.

David Cameron is backing the inclusion of the Greens in the debates, claiming it would be unfair to leave out one minor party when Ukip and the Liberal Democrats would be invited by the broadcasters to take part.

However, Ed Miliband, the Labour leader, claimed 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.

This article was amended to reflect the fact that the SNP has more members than the Greens, but is not a UK-wide party.