The businesswoman led and won two legal challenges to the UK government’s Brexit strategy.
Cartmel Racecourse has apologised after a tweet went out on its social media account abusing the campaigner, Gina Miller.
Two abusive messages were posted after Ms Miller's appearance on the BBC TV programme Question Time.
The racecourse management says it has established that the post was not from a member of staff, but resulted from "unauthorised access" to its account, and an internal inquiry was taking place.
The offensive tweets have been deleted.
You can watch the show below:
The campaigner says she watched the ill-tempered debate in the commons on Wednesday in "total horror and disgust".
The Supreme Court will rule on Tuesday whether the PM's decision to suspend Parliament was lawful