This marriage in Pallots index took place 40 years before the period 1837-1839 you specify. FreeBMD coverage 1837-1839 is complete for the GRO civil registration index except for the quarter December 1839. Checking the actual GRO index for that quarter there were no Henry Brindley marriages - so it looks like your marriage may very well have been pre civil registration (starting 1st July 1837)
Pallots
Henry Brindley Anne Hunt 1790 Marden Wiltshire
Regards
Valda