In a study of 57 Tory seats, 38% said Sir Keir would be the best Prime Minister, while a majority doubt Boris Johnson would be in Downing Street next year.
It is a political phrase denoting traditional Labour strongholds in the Midlands, Wales and northern England.
The Deltapoll poll for the Mail on Sunday also put Labour ahead in those seats (49 percent vs 33 percent ).
Meanwhile, it showed Labour five points ahead overall (40 percent vs 35 percent ).
If the results hold in a General Election, the Conservatives might lose over 100 seats.
Sir Keir's vote would get him into Downing Street, but not a majority.
Tories gained seats preferring Sir Keir and shadow chancellor Rachel Reeves (40%) to Mr Johnson and Rishi Sunak (33 percent ).
When asked if Mr Johnson was performing well overall, only 34% agreed, while 62% disagreed, giving him a net rating of -28.
Sir Keir got a minus 6 as well.
The PM's situation worsened when voters in 57 seats were asked about the pandemic. Only 32% agreed, while 62% disagreed.
Only 16% thought Mr Johnson followed the rules, while 72% did not.
When it comes to Covid limitations, a majority (65%) thought the PM should resign.
In contrast, when it came to Mr Sunak's pandemic performance, 45 percent agreed with him, while 40 percent disagreed.
Just 24% of respondents in Tory-held seats thought Mr Johnson would still be in charge next year.
Most (58%) anticipated he'd be replaced, and over three-quarters (74%) said they didn't trust him to tell the truth.
Conservative MP Lee Anderson claimed some first-time Conservative voters were beginning to doubt themselves.
My voters care far more about rising energy bills than the cliches spouted about the “green agenda” by the wealthy elite who flew into the Cop26 meeting in private planes,' he said.