The Prime Minister also faces the loss of Wakefield to Labour in a pair of by-elections which could lead to further questions about his leadership.
Ballots were cast in Wakefield and Tiverton and Honiton after contests triggered by Conservative MPs resigning in disgrace.
With official results yet to be declared, the Liberal Democrats claimed victory for candidate Richard Foord in the Devon seat – which had been held with a majority of more than 24,000 by the Tories in 2019.
A Lib Dem spokesman said: “This is looking like a clear win. The people of Tiverton and Honiton have spoken up for the country.
“This is an historic victory for the Liberal Democrats and a devastating blow for those Conservative MPs who continue to prop up Boris Johnson.”
Defeat for the Tories will heap pressure on Mr Johnson just weeks after 41% of his own MPs said they did not have confidence in him.
Mr Johnson, who is at a Commonwealth leaders’ summit in Rwanda, suggested it would be “crazy” for him to quit if the party lost the two seats.