Connolly, 69, walked off the stage 20 minutes early at a Blackpool gig last weekend and he cut short a performance in Scarborough a few days before that, the BBC reported.
The actor/comedian was tightlipped about the incidents, but an unnamed spokeswoman for Connolly said he'll pick up his tour Friday in Llandudno, Wales.
One fan who caught Connolly's Blackpool show said he walked out after a heckler interrupted one of his jokes.
"It was such an anti-climax and I felt he should have been used to hecklers," Ffyona McKeating said.
At the Scarborough gig Connolly allegedly left the stage because he was upset at drunk and rowdy patrons heckling him and leaving their seats during the show to go to the bar, the BBC said Friday.
"The bar should not be open when a show is running. People constantly got up out of their seats and it was extremely disrespectful to Billy," one unnamed fan said.