The Glos OPC site will certainly help with searching before 1837, but not so much in this case as Bremhill is in Wiltshire
William and Eliza have two children born after 1837 so the first thing to try is their birth certificates. The GRO's online index shows them both, with mother's maiden name Rivers. The eldest child is 8 so you want to look for a marriage 9 or 10 years earlier. The Wiltshire OPC does have registers for Bremhill so you can look there, but while you have access to Ancestry that's easier and gives you an image of the record as well. William Summers, of Bremhill, married Eliza Rivers from Seend at Bremhill on 20 Oct 1832.
Ancestry also has over a hundred member's trees that include William and family. You can ignore them if you want the fun of doing it all yourself. If you do use them, bear in mind that they are invariably full of mistakes, double check everything.
Happy hunting
David
