She told detectives at Staffordshire Police that he was one of a number of men .
She believes a Lord and a judge may also have been among her abusers.
Ms Baker described the political figure as: "One of the core members. He was there quite often - I was one of his favourites.
"I used to play the piano, and he was quite taken with that ... there were different houses.
"I would sit on his lap and he would want me to play."
The politician is not from Staffordshire but is from the current political era.
Ms Baker has given a graphic and detailed account to detectives and explained to them how she only recently realised who the man was.
She said: "I would know that face anywhere. I have lived with it and others in my head for over 20 years, I know every inch of him."
Urging other potential witnesses or survivors to come forward, Ms Baker said: "I always swore I would never go near the police again - never.
"I was scared because it feels like, yeah, they are going to know I have said something so the only way I can now protect myself is now to tell.
"I just hope others will do the same. That is the only way we are going to be safe."
Ms Baker has ongoing support from the Lantern Project on Merseyside, which works with survivors of sexual abuse.