Tom Blenkinsop, a fierce critic Mr Corbyn, spoke out after the Conservatives won the Coulby Newham by-election to Middlesbrough Council with a swing of more than eight per cent.
Mr Blenkinsop, MP for Middlesbrough South and East Cleveland, said: "We lost due to the leader's name being mentioned on the doorstep as the reason why residents were not voting Labour.
"And I am certain this is not just the case here but across boroughs and constituencies the length and breadth of Great Britain."
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We lost due to the leader's name being mentioned on the doorstep as the reason why residents were not voting Labour
He said since at least 1999 the ward has elected either three Labour councillors or two and an independent.
Labour insiders insist leadership change is not the answer to the party’s problems.
A party source said the Middlesbrough result was close on a low turnout and that the party had gained more council seats this year than it had lost.
Jeremy Corbyn's Labour Party face a disastrous showing at next month's local elections
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The source said: "The Middlesbrough by-election was very close – only 33 votes separated Labour and Conservatives – and the turnout was extremely low making it difficult to draw any meaningful conclusions.
"However, voters don't like divided parties, public attacks and infighting.
"Unity is essential to delivering effective opposition."
The Middlesbrough result follows the Tory capture of Copeland which had been a safe Labour seat since 1935 until February’s by election victory for Trudy Harrison.
Jeremy Corbyn with railwaymen in Doncaster Corbyn looks crushed following by-election defeat Fri, February 24, 2017
Labour leader Jeremy Corbyn leaves his home following a humiliating blow by the Conservatives after snatching Copeland in a by-election victory. The struggling politician was talking on the day his party lost a by-election to the government, the first time this has happened in over 30 years.
Adam Gray / SWNS.com 1 of 10
Jeremy Corbyn is seen at Savoy Place in London where the Labour leader was giving a speech on Brexit
Election experts say Labour faces its worst local elections drubbing in 35 years next month because of its nosedive in the polls.
Hapless leader Mr Corbyn is expected to lose 125 council seats on May 4.
The losses would be the biggest suffered by the main opposition party since 1982, when the Falklands War was raging and Margaret Thatcher was in her pomp.