Councillor Pervez Choudhry, 52, was arrested on Monday and later released on bail.
Choudhry, who was originally elected as a Labour candidate for the Central Ward but later defected to the Tories, is due to appear at Maidenhead Magistrates’ Court next Monday.
Peter Dale-Gough, the acting leader of the Conservative group on Slough Borough Council, said Choudhry had told him that he took part in a religious ceremony to his first wife but never went through with the civil ceremony and was therefore not married by law.
His second wife, a GP who was said to be about 10 years his junior, lives and works in Birmingham. He was said to have met her while using an online dating site and married her in Pakistan.
She was thought to have left Choudhury on learning that his previous marriage may not have legally ended.
Choudhry, of Slough, has vowed to clear his name, after agreeing to stand down as the Conservatives’ leader.