The Bill had proposed that the Lords' membership be reduced from 826 to 450, and that 80 per cent of members be elected and the remaining 20 per cent appointed.
It also proposed reducing the number of bishops from 26 to 12, to reflect the smaller size of a reformed Second Chamber.
On Monday, the Deputy Prime Minister, Nick Clegg, announced that the Bill had been abandoned because the Prime Minister had been unable to persuade a sufficient number of Conservative MPs to support it.
Mr Clegg said that the Government did "not have the Commons majority needed to ensure this Bill progresses through Parliament. It is obvious that the Bill's opponents would now seek to inflict on it a slow death: ensuring Lords' reform consumes an unacceptable amount of parliamentary time." He said that "an unelected Lords flies in the face of democratic principles and public opinion".
Responding to the announcement, the Bishop of Leicester, the Rt Revd Tim Stevens, who acts as the bishops' convener in the Lords, said: "Having served on the Parliamentary Committee looking at the Government's draft proposals, I know that some of the more complex and important questions about the implications of the reform plans had not been resolved, and I understand, therefore, the lack of a consensus.
"Reforms that would have seen a simple substitution of the existing House for a largely or wholly elected Chamber risked both removing what is best about the present Lords - the independence and expertise that its membership brings to bear - and undermining the current conventions between the Houses that prevent damaging gridlock between the Commons and Lords."
Bishop Stevens said that the decision not to proceed with the Bill "gives Parliament and the country a welcome opportunity to pause and think again about what it wants a Second Chamber to do. . . It also means that Parliament will be able to focus without distraction on the most pressing economic and social challenges that face our country now and in the months ahead."
Bishop Stevens said that the Lords "still needs a measure of reform, not least to formalise its disciplinary procedures and to resolve the problem of its ever-increasing size". He described Lord Steel's Private Member's Bill, which contains more modest reform proposals, as "certainly worthy of support".
Giving evidence to the Joint Committee last year, the Archbishop of Canterbury said: "The bishops are not there to represent the Church of England's interests: they are there as bishops of the realm, who have taken on the role of attempting to speak for the needs of a wide variety of faith communities."