The general secretary of Labour's biggest union, stung by claims that his organisation, Unite, has been fixing the selection of parliamentary Labour candidates, has turned the tables on a billionaire backer and a Blairite thinktank, accusing both of manipulating selection procedures to install favoured centre-left MPs.

Len McCluskey, writing in the Guardian, said that Lord Sainsbury had worked with Progress to pour funds into Labour's headquarters that have helped to "parachute" favoured candidates into safe seats – meaning that the parliamentary party is out of touch.

"It is past time that the spotlight was shone on the activities of Progress, largely funded by Lord Sainsbury, which has been sparing no expense to get its candidates adopted. The Sainsbury 'block vote' has been used to create a parliamentary Labour party that does not look like, or think like, the party more broadly," McCluskey writes.

The uncompromising comments show that despite efforts to heal the wounds with Ed Miliband, the union leader wishes to continue his political battle with centre-left Labour supporters who wish to curtail Unite's influence.

"This does not end the right-wing's manipulation of selection procedures. Every manoeuvre has been deployed, often with the assistance of Labour headquarters, to 'parachute' favoured candidates into safe seats. Until our Blairite critics face up to the serial abuses of party democracy associated with the New Labour years, they cannot be taken seriously as reformers," he added.

His claims come after Labour handed evidence to police in Scotland about claims that Unite associates tried to fix the result of a candidate selection in Falkirk by packing the constituency with members, whose subscriptions it paid.

McCluskey said in the article that, as far as he knew, his associates had done nothing wrong in Falkirk. In fact, he wrote, they were only trying to enact a union policy to try to back MPs from working-class backgrounds. "The underlying politics include the need to radically broaden the range of people serving in parliament, and to re-engage with the growing proportion of the electorate now alienated from the democratic process," he writes.

He argued that by contrast Unite had been "doing far less than the well-funded standard-bearers of the New Labour status quo" with "our members participating and our funding accounted for". He added that "a universally-applied spending cap which levels this playing field could well be a step forward".

Observers say that the union is in the midst of a backlash against the previous era of Tony Blair, when the former Labour leader chose to define himself against the unions. Blair flaunted his dislike for the close relationship which had existed between unions and Labour leaders going back to Harold Wilson and instead brought in more donors from big business.

As a result, most unions, under pressure from increasingly angry activists and diminishing power and membership, drifted to the left and lost patience with their traditional allies in Labour.

Centre-left Labour activists also point to individuals who they say have too much influence over McCluskey. One of those criticised is Andrew Murray, the leader's chief of staff and a former Transport and General Workers' Union official who is a member of the Communist party of Britain.

But Murray's friends say that McCluskey, softly spoken and well read, thinks for himself and employs Murray for his organisational abilities, not his views.

While McCluskey is attacked from the right in the Labour party, his more prominent critics from inside Unite come from the hard left. Jerry Hicks, who received 80,000 votes when he stood against McCluskey in April, said that the union leader's overly cosy relationship with Labour has left both the union and the party open to criticisms of backroom deals.

"We should have used our £8m of donations to fundamentally change our relationship with Labour. We should insist on more MPs who will argue in favour of our members and our beliefs, and do it openly and fairly and through negotiation," he said.

Sainsbury, who was science minister under Blair and gave the party £18.5m, has stopped funding since Ed Miliband beat his brother to Labour's leadership, aided by Unite funds. His office did not respond to requests for a comment.

A spokesman for Progress said: "Progress helps to train and mentor candidates going for selection, to whom we do not give money. The details are open, plainly explained on our website and approved by a strategy board elected by our members. These comments are little more than a desperate smokescreen."