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There is no offence of polygamy as such. A person who enters into a second or subsequent marriage while the first is still valid commits an offence of bigamy under section 57 of the Offences Against the Person Act 1861.
The most recent data available, from the court proceedings database held by the Office for Criminal Justice Reform, show that in England and Wales in 2005, 28 defendants were prosecuted for and 21 found guilty of the offence of bigamy. Data for 2006 will be available in the autumn of 2007 and data for 2007 will be available in the autumn of 2008.