I have Kent Family History Society parish register transcriptions for both Boughton Malherbe and Lenham.
These seem to be the marriages of the 2 sons you mention, at BM;
1754 Feb 22 John SEDGEWICKE of Lenham married Mary ELSE otp
1759 Aug 20 Richard SEDGWICK of Lenham bachelor married Jane ELSE otp spinster by Banns
As to the parents it is quite difficult to search the registers because there are lots of name variants - SEDGWICK, SEDGWICKE, SEDWICK, SEDGWICKS, SEDWIX etc.
I can't see a suitable marriage at BH or L for the couple. I only have transcriptions for marriages at BH so cannot check for baptisms. I can't find any SEDGWICK or PAGE baptisms at Lenham around 1710, but there appears to be a gap in the registers between 1709 and 1711! Again another gap between 1728 and 1735! I can't see a baptism for a Richard SEDGWICK around 1740.
There are these burials at Lenham;
1747 07/02 Jane SEDWICKS Wife of John
1755 07/21 Edward SEDWIX Son of John and Anne
1757 03/06 John SEDGWICKS
Hope these might help.