Minister have been warned they cannot "wash their hands" of responsibility for keeping inflation under control.
Ex-Treasury minister Lord Myners said the Bank of England seemed "unable" to meet the 2% inflation target and urged ministers to intervene.
City minister Lord Sassoon told peers he was "concerned" about the impact of rising prices but had "every confidence" in the Bank of England.
The consumer prices index rose from 3.4% to 3.7% last month.
Bank of England Governor Mervyn King is required to write to the Chancellor every time the inflation target is missed by one percentage point either way.
The Bank's Monetary Policy Committee has come under pressure from some to raise interest rates - which have remained at 0.5% for more than 18 months - to help contain inflationary pressures driven by rising fuel bills and food costs.
During a brief debate on the issue in the Lords, peers from all sides of the House expressed concern about the impact of price inflation on living standards.
Tory peer Lord Spicer said it was time for policymakers to consider tightening monetary policy while Lord Myners suggested that the Bank was failing in its duty when it came to inflation.
"The government cannot wash its hands of any responsibility for inflation," he said. "What is the government going to do about the inability of the MPC to hit the target which it has set."
The explanations given by Mr King for the rate of inflation had become "anodyne and routine", Lord Myners suggested, while little seemed to be being done to reduce it.
But Lord Sassoon said the Bank had been forced to write to Labour Chancellors five times between 1997 and 20120 and he did not "recall the previous government doing anything about it in response".
"Of course the government is concerned about the current level of inflation and the impact it has on many parts of society, particularly working families and on savers," he said.
"I am very happy to confirm that the government has every confidence in the Monetary Policy Committee and absolutely recognises the independence of the MPC as a cornerstone of making sure the chancellor's inflation target is hit."
Ministers had set a "firm policy background" for the Bank of England to deal with inflation, he said, in terms of reducing borrowing and stimulating economic growth.
For Labour, Lord Davies said rising inflation had a "particularly savage" impact on the livelihoods on the least well-off in society.
But former Treasury minister Lord Barnett urged ministers not to "wrongly pressurise" the Bank of England into raising interest rates prematurely.
The Monetary Policy Committee has said it believes spare capacity in the economy will bring inflation down closer to the 2% target in the medium term.