Pervez Choudry (Tory at time of the charge)
Councillor Pervez Choudhry, of Tuns Lane, Slough, was arrested and charged with one count of bigamy in August 2010.
The 53-year-old defected to the Tories in 2009 after being elected as the Labour candidate for Central Ward, but is now an independent councillor.
Mr Choudhry will be sentenced at Reading Crown Court on Friday 18 May.
His term of office runs until 3 May.
Mr Choudry said he was unable to comment because it was a "sub judice matter" but that "this case has no bearing or will have no bearing on my standing as a councillor".
Slough Borough Council said it was a "private matter".