There are three possible WIlliams. The one that is documented in the Events and the following two which also less than 2 miles from Bermondsey.

Call the one in Events as #1 with #2, and #3 below. I think we can eliminate #2 as he would have been 17 at marriage. Of the others, #1 seems still young as he would be 19 at marriage. #3 seems most probable as he would be 24 at marriage.

#2
First name(s)
William
Last name
Reed
Birth year
-
Baptism year
1747
Baptism date
01 Mar 1747
Baptism place
Rotherhithe St Mary
Relationship
Son
Father's first name(s)
Francis
Mother's first name(s)
Mary
County
Surrey
Country
England
Record set
Surrey Baptisms
Category
Birth, Marriage & Death (Parish Registers)
Subcategory
Parish Baptisms
Collections from
England, Great Britain

#3
First name(s) William
Last name Reed
Birth year -
Baptism year 1740
Baptism date 26 Jun 1740
Baptism place Rotherhithe St Mary
Relationship Son
Father's first name(s) George
Mother's first name(s) Mary
County Surrey
Country England
Record set Surrey Baptisms
Category Birth, Marriage & Death (Parish Registers)
Subcategory Parish Baptisms
Collections from England, Great Britain