Peers have voted to censure Lord Clarke of Hampstead after an inquiry found he claimed overnight subsistence payments for nights when he did not stay in London.
The peer, who was suspended from the Labour Party following the allegations, apologised to the House "without reservation for my misuse of the members' reimbursement scheme".
"I very much regret the damage that has been caused to the reputation of this House," he added.
After the apology, government whip Lord Bassam of Brighton outlined details of legislation for consideration in the upper chamber in the short period before Parliament is prorogued for the general election.
Lord Bassam revealed that ministers had dropped plans to hold a referendum on using the "alternative vote" system for future Westminster parliamentary elections.
A bid to phase out hereditary peers from the Lords would also be abandoned, he said.
Both of the proposed changes to the Constitutional Reform and Governance Bill had come under fire from opposition parties.