He used the word to refer to the people of Blackpool.
In a statement, Borthwick admitted his use of the slur was unacceptable.
“I want to apologise sincerely and wholeheartedly for the words I used in the video showing my reaction to making it through Blackpool week on Strictly,” he said.
Borthwick competed on Strictly Come Dancing with dancer Michelle Tsiakkas. Photo / Michelle Tsiakkas
“I am deeply sorry for any offence and upset my words and actions have caused. It is no excuse, but I did not fully understand the derogatory term I used and its meaning.”
Disability charity Scope told BBC News they hope the actor “takes the opportunity to get to know the reality of disabled people’s lives”.
Borthwick was already at the centre of another Strictly debacle before the leak.
A video of him behind the scenes of the show’s live tour showed him holding a sex toy sent by fellow contestant Wynne Evans.
“Look at what he bought me,” Borthwick said in the clip, “I opened it up and he surprised me with this, didn’t he? It’s so funny.”
Evans was later dropped by the BBC for behaviour on the show they deemed sexually inappropriate.
Borthwick was one of the longest-running cast members on EastEnders and had won a British Soap Award for the role.