Andy Burnham is the top choice of Labour members to succeed Sir Keir Starmer as prime minister. The Mayor of Greater Manchester was the first choice of 29% of members.
Deputy Prime Minister Angela Rayner was in second place in the poll of Labour members by Survation for LabourList.
Health Secretary Wes Streeting is in third place - the top choice of 8%.
Home Secretary Yvette Cooper and Left-winger Clive Lewis are tied on 5%.
Energy Secretary Ed Miliband was the choice of 3%.
Mr Burnham was Health Secretary under Gordon Brown and stood for the leadership in 2010 and 2015. He was elected Mayor of Greater Manchester in 2017 and won UK-wide attention during the pandemic.
The country gained an insight into Deputy PM Ms Rayner's activities behind the scenes in cabinet last month when a leaked memo revealed she had pushed Chancellor Rachel Reeves to raise taxes. Her proposals included increasing corporation tax on banks.
Mr Streeting, who is known for his willingness to embrace the private sector in the NHS, is seen as a leading figure on the Right of the party.
Survation surveyed 1,304 readers of LabourList who were self-declared Labour members between May 30 and June 1.