Creative differences and the limited strategic input required from the agency on the business in recent months are cited as the reason for the parting, which both sides describe as "entirely amicable".
News of the parting comes shortly before the debut of a new 12-sheet poster campaign by the agency to promote the waxworks' latest attraction - a whispering and breathing model of Kylie Minogue.
The posters depict the pop star's famous rear and a pull-cord hanging down her back with the line: "Kylie now talks at Madame Tussaud's."
BMP took over the account in November 2000 from J. Walter Thompson, which produced a series of award-winning ads during its six-year tenure of the business.
At the time, Madame Tussaud's cited BMP's "creativity and enthusiasm" as the reason for the appointment. It was seen as a precursor to making the attraction more appealing to adults and raising its domestic profile, while maintaining its popularity with overseas visitors.
BMP will continue to handle the business until the end of the year to give Madame Tussaud's time to make alternative agency arrangements.
Industry sources say the parting was prompted by the changing needs of Madame Tussaud's. It is said to have appointed an internal consultant, leading to less reliance on BMP for strategic advice and a reduced need for a full-service agency.