Bamford, who has substantial business interest in India, had his nomination rejected by the House of Lords Appointments Commission after the tax authorities failed to support it.
Earlier, the Conservative-led coalition Government in Britain was rocked after Chief Treasury Secretary David Laws resigned over his expenses scandal.
Laws, the Treasury Minister in charge of cutting public spending, quit last night after it was reported that he had directed more than 40,000 pounds of taxpayers' money to his secret gay lover. His decision after 17 days in the jobs means Laws had the shortest Cabinet career in modern political history.
The rejection of Bamford's application comes as a blow to Cameron who had personally recommended him for ennoblement. It will raise further questions about the funding of political parties and the rewarding of donors with honours.
Days before the list was published on Friday, Bamford wrote to Cameron withdrawing his name from the process.
He said he wanted to concentrate on running his company. A spokesman denied his withdrawal was anything to do with his name being vetoed by the appointments commission.
He said he was unaware that any concerns had been raised about his tax affairs.
The Bamford family has donated generously to Tories. Bamford's firm has given the party 1.5 million pounds, while Bamford, 64, has donated 86,000 pounds including 10,000 pounds worth of helicopter rides to Cameron.
The businessman, whose wealth is 950 million pounds, according to the Sunday Times rich List, was awarded a knighthood in 1990.
A spokesman for Bamford said: "Sir Anthony was approached by David Cameron six months ago to be a working peer with a brief for manufacturing and engineering.
"However, he has decided he would not be able to devote the time to the House of Lords and feels that he still needs to commit full time to the affairs of the JCB group.
The new Tory, Lib Dem coalition government assumed office on May 11 under the leadership of Cameron who assumed office as country's Prime Minister.