A row over trade union influence in the selection of Labour parliamentary candidates has intensified after the former home secretary, David Blunkett, warned that the party was in danger of ending up in the "graveyard".

Britain's largest trade union – which has been accused of packing the local Falkirk Labour party with its supporters – stepped up the pressure when it called on the leadership to reverse its decision to take control of the selection of the candidate in the constituency.

In a lengthy statement Unite said: "The imposition of a regime of 'special measures' on the CLP [Constituency Labour Party], are unnecessary and are at best an extreme over-reaction, at worst the product of an anti-union agenda."

The union, whose general secretary, Len McCluskey, recently warned Ed Miliband not to be seduced by supporters of Tony Blair, issued its statement after Blunkett warned that such thinking posed a grave threat to the party.

The former home secretary told the Daily Politics on BBC1: "We don't want to go back to divisions and diversions of this sort. We are a broad church, we should be and we should be able to welcome and engage with a whole range of people. We shouldn't be afraid of ideas and policy. At the moment, if we are afraid of those and the idea of looking to the future and being radical then, I'm afraid, we'll be the party of the graveyard and none of us want that."

The Labour movement has been engulfed in one of its most serious rows after the party's national executive committee (NEC) took control of the selection of its general election candidate in Falkirk amid accusations that Unite has packed the constituency with supporters.

The NEC announced last week that it had found "sufficient evidence for concern" about the way in which members were signed up for the Falkirk CLP.

Unite is alleged to have recruited hundreds of its members to the Falkirk party, which has to select a new Labour candidate for the 2015 general election after Eric Joyce announced he would be standing down after a fracas in a Commons bar. The union is alleged to have sent a covering cheque to pay for membership fees, rather than allow individual members to sign a direct debit mandate.

The name of Karie Murphy, who is a former Unite official and aide to the Labour deputy chairman, Tom Watson, and who was the frontrunner, will not appear on the all-women shortlist for the Falkirk selection. Under the "special measures", the Labour NEC has the power to draw up the shortlist.

The latest row came after the Times published the minutes of Unite's executive council meeting on 3 December 2012, which described the handling of the membership drive in Falkirk as "exemplary". It said there were another six constituencies – Peterborough, Norwich South, Harlow, Hastings, Tamworth, and Crewe and Nantwich – where the union is having a "direct impact".

The Times quoted the document as saying: "This is not an exhaustive list of the better candidates." It added that, without the support of the union, the Blairite thinktank Progress "or other rightwing candidates would have been selected".

Grant Shapps, the Tory chairman, said: "Day by day an unaccountable and unelected union baron is strengthening his vice-like grip on the Labour party. If Ed Miliband won't stand up to the likes of Len McCluskey in his party, there's no way he could stand up for the interests of this country."

Jake Berry, parliamentary private secretary to Shapps, has written to the information commissioner, Christopher Graham, calling on him to investigate whether Unite has breached the data protection act. Berry cited an article in the Sunday Herald in May, which said that three members of a family were recruited to join the Falkirk CLP even though only one agreed to join in principle.

Labour said it had taken decisive action after an internal report said there was sufficient evidence to raise concerns about the recruitment of party members in Falkirk. It had placed the selection process in special measures and decreed that no member who joined after 12 March, the day Joyce announced he would stand down, could vote in the candidate selection.

A Labour spokesman said: "Throughout this matter the leadership has acted in a swift and thorough way to protect the integrity of the Labour party."