with apologies for not having checked the link on the previous post so this duplicates some of it.
According to some of the unsourced ancestry trees I saw on Ancestry ), this family was from Brinkworth, Wiltshire. There are transcribed registers for Brinkworth on the Wiltshire OPC
John's son Anthony was baptised in Brinkworth in 1697 (the date on the profile)
1697 07-Feb Spencer Anthony, M, Spencer John Spencer Ann
There was also a John s of Francis baptised in 1667
1667 21-Mar Spencer John, M, Spencer Francis
Also an Emma d of Francis baptised in 1661
At a quick look, I can't find either a marriage or banns for an appropriate John and Ann or Francis and ? ( various Johns and Marys and one John Spencer to an Ann Ayliffe but that was in 1620 so too early for this John and Ann.) Edit Just found "1633-1652 - Marriage Register missing or unavailable" and "1605-1632 - Marriages recorded from the Bishops Transcripts"
The baptism records do not go back far enough for the birth of Francis)
I didn't see any Spencers in the two Manorial rent documents transcribed on the site. It would be worth looking at the wills on the site (sons 'in law' are often mentioned)
I did notice that one Spencer came from Dauntsey, which is 'next door' so that might be a place worth looking at. (the other neighbouring villages are listed on the page, ) One Spencer in the records gets a title (Mr) and another was a yeoman but the others are labourers. It may be family in the area with lots of branches. (or just a common name!)