The former Lord Mayor of London said he was warned by the then Bank of England governor Mervyn, now Lord King, that a political decision had been made to sell the 631 branches to the Co-op.
At a highly-charged session of the Treasury Committee, Lord Levene also disputed claims by Lloyds, the owner of Bank of Scotland, that it did not receive an NBNK document warning of problems with the Co-op bid in early 2012.
"I believe Lloyds were swayed by political considerations," Lord Levene told the committee.
He added: "In our view they chose to concentrate on all the positive aspects for the Co-op and none of the positive aspects of our bid."
Lord Levene said there was a view, in Government, that a successful Co-op bid for the Lloyds branches would be "another tick in the box" of the Coalition agreement that pledged to support mutual institutions.
Key figures such as Business Secretary Vince Cable and Treasury minister Mark Hoban were enthusiasts for the Co-op, he claimed. He also accused Lloyds of "unattractive commercial practice".
"If you say to me 'do you think it (the bidding process) was bad faith?' Yes, I do," he said.
He ruled out taking legal action, despite losing £60,000 of his £100,000 investment in NBNK.
However, he said some NBNK investors, who include Edinburgh house Baillie Gifford, were considering whether to go to court to recover £30 million in losses.
Lord Levene said that part-nationalised Lloyds had made a "miscalculation" in its assessment of the value of the two bids, despite changing deadlines and the form of the Verde business in what he believed was an effort to make things easier for Co-op. Lloyds has always insisted that it chose Co-op because, with an existing bank, it was better placed to execute the merger.
Lord Levene, former chairman of the Lloyds insurance market, said Lord King had called him to a meeting in May 2012 to tell him the Verde sale was "a political decision and the only way forward was to talk to the politicians". Lord Levene added: "He said that the decision had been made to give the contract to the Co-op."
Gary Hoffman, who was paid £750,000 a year as chief executive of NBNK, said: "It was crystal clear that the execution risk with the Co-op was extremely high."
Co-op's attempted purchase collapsed in March last year and was followed by revelations that it required £1.5 billion in capital as it struggled with losses on property loans. The subsequent reconstruction of Co-op Bank has given majority control to the hedge funds who own its debt.
Lord Levene insisted he had handed a paper copy of NBNK's risks document on Co-op to Lloyds chairman Sir Win Bischoff at a meeting also attended by Mr Hoffman in January 2012.
"Maybe he had a senior moment. Maybe it dropped down the side of a sofa," Lord Levene said. "If he said I did not give it to him, that is not true."
It was too sensitive to send electronically, he said.
Lloyds continues to maintain that Sir Win received no document from NBNK, whose directors included Scottish politicians Lord Forsyth of Drumlean and Lord McFall of Alcluith.
Mr Hoffman admitted to MPs he had held talks with Co-op about becoming chief executive of its bank, but said he rejected a move while the NBNK bid was still live.
Lord Levene said: "People have accused me, accused us of being bad losers. We were not bad losers. It was an appalling winner."
Lloyds has since rebranded Verde as TSB and plans to list it on the stock market.
Lord Levene suggested this might have been Lloyds's preferred approach from the start.