The data for John Spooner the schoolmaster in Southwark/Camberwell seems to hang together well enough. But I can’t see that there is any real evidence to connect him to your ancestor William Spooner, the linen draper/commission agent in Clerkenwell.
Looking more closely at your Spooner family in Clerkenwell in 1841, there is a son Henry aged 15+. He appears to have been baptised in 1827 at St Luke’s as Henry Hodgkin Spooner, son of William, linen draper, and Catherine (who is not showing in the 1841). That points to a possible marriage in 1811 in Edenham, Lincolnshire, of William Spooner and Catherine Hodgkin.
https://familysearch.org/ark:/61903/1:1:NVGQ-WXV
Their son Frederick William, aged 25+ in 1841, was baptised in Edenham in 1814 (FamilySearch).
Have you already searched in Lincolnshire for a baptism for your William Spooner?
ADDED - if you do want to pursue the Spooner family from Towcester, you may want to post on the Northamptonshire board, as I believe there is a RootsChat member with expert knowledge of Towcester.
Hello There,
I had already searched for baptisms of William Spooner born in Lincolnshire, around 1787, and found nothing. I knew that he married Catherine Hodgkin, in Edenham in 1811. His abode on the marriage Licence was: "Cateaton Street, in the parish of St Lawrence, London".So my William was already in London by this time.
Also, William's year of birth on the Marriage Licence, in December 1811, when he married Catherine was put down as 1787. This is the same year as the baptism I found for William Spooner, baptised in Towcester. Also, William Spooner died on February the 17th 1845, and his age was put down as 58. This may also give his year of birth as 1787. He could have been born early in that year, and then baptised in Towcester, on August the 24th.
I knew from the 1841 Census, that William Spooner was not born in Middlesex.
I looked up other William Spooner's baptised in other Counties around the same time mine would have been born from baptisms in: Norfolk, Kent, some in Essex, one in Suffolk also. I found them all in the 1851 Census. There were two baptised in London in 1789, and one in Chelsea in 1787: The fact that I knew he was not born in Middlesex, I knew I could dismiss those as a possibility also.
I went onto Freereg. On there I found a baptism for William in Towcester, in 1787, the son of a Sarah, and John. So I went back to the menu and typed in the search part: "John Spooner" 1783 - 1840" for Northamptonshire, and put down to include "family members". It came back with the marriage of John Spooner and Sarah Kingston in 1785, in Towcester, and all the children that they had. Those included William in 1787, and John, baptised in Towcester in 1792.
Those search results that came up also only went up to the burial of George Spooner, in Towcester, in 1796; This would suggest that the family possibly then went elsewhere.
I looked into the parents of this John and William. John Spooner was baptised in 1755, in Towcester, and married Sarah Kingston, in 1785. Sarah Kingston was baptised around 1761 in Towcester. I found a burial for a John Spooner at Clerkenwell, buried in 1829, and his year of birth was put down as 1755. I also found a Sarah buried there, and her years were: 1763 - 1824.
I know for a fact from the "Old Bailey Online Proceedings", that William Spooner had a Brother called John. There is also a very good chance from reading this, that this John was also probably a Linen Draper:
https://www.oldbaileyonline.org/browse.jsp?id=t18161204-41&div=t18161204-41&terms=William_Spooner#highlightThe John Spooner that I found had been a Linen Draper.I know that from the baptisms of his Daughters. The same John Spooner went on to become a School Master. I know that from marriage certificates of his daughters, and from census returns.
He was also living quite near to William Spooner, just across the other side of the Thames. So he would have lived near his brother.
This John Spooner was also born in Towcester, baptised in 1792, and he had a Brother called William according to Freereg. And the year of baptism that I found for William in Towcester is consistent with information I found on William's Marriage Licence, and the Death Certificate.