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You do not have to have a religious ceremony.  You can hold your wedding in numerous local places, including register offices, hotels, castles, town halls, stately homes etc..

Approved venues in England and Wales
A full list of approved venues throughout England and Wales is available from the Office for National Statistics.

You can find your local Register Offices on their website.  Simply enter your postcode or a postcode for the area where you would like to marry on www.statistics.gov.uk/registration

Alternatively useful information, including lists of various wedding venues can be obtained from the County Council websites.  Some examples are

www.westsussex.gov.uk

www.eastsussex.gov.uk/community/registration
or
www.eastsussex.gov.uk/community/eventsinyourlife/gettingmarried

www.surreycc.gov.uk  enter community then birth death and marriage

www.kent.gov.uk/community/biirths-marriages-and-deaths