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John COOK married Martha AVIS in St John Horsleydown, Southwark 4th Aug 1743.
Certainly 2 but probably 3 children are identified as their children baptised In the same or adjacent  parish, but the first child almost 5 years after their marriage , and a gap 1752 to 1761.
For both early bapts John 's occupation is detailed as plaisterer, ( no identified Guild record yet)
Daughter Avis on 14th April 1748, buried 11th June  1748.
John Robert 1st July 1750.
Possibly Martha Mary 15 June 1763, St Mary Magdalene, Bermondsey, Southwark, Surrey, England, abode Holly, but occupation Porter.
There are baptisms for another 3  children to a John and Martha in this general area, that are probably not the same couple, but a John COOK and Martha PRYKE married 12 May 1759 in Holborn
Elizabeth Skelton 29th Aug 1759, father is John (elder) St Paul, Shadwell, Tower Hamlets, no occ for father.
Esther 25 Dec 1760,  St James, Clerkenwell
Elizabeth 12 Feb 1767 St George the Martyr, Queen Square, Camden, Middlesex.
The main question is what adjacent or close parishes are not currently covered on the main Genealogy sites as searchable records.
This might allow those parishes to be targetted and checked for additional siblings.
It is possible that John and Martha migrated, and specifically to Kent. The occurrence of the name Avis as a forename in a COOK family in Kent might be a link, and is the catalyst for this family to be researched as potential ancestors . A previous posting of COOK in Brasted Kent is part of the overall research.
Martha's AVIS family appears to be identified in St Olave, but is not the intended target for this post.
If current records on line  are anywhere near complete, it would seem that Martha'' parents , Robert ( occ baker) and Mary married in Withyham, Sussex, before migrating to Surrey, this seems plausible as Robert and Mary don't appear to feature in baptisms in Sussex after their marriage.

Eliza COOKE was probably born in Kent to a John and Ann. Eliza is believed to have had a sister Sophia who married in Isfield on Xmas day  1820 to Jacob WELLS when she is a named as a witness. She later married Francis WELCH in Isfield on 17 Dec 1822 and had a family of 8 children. In 1841 she is with the family in Frant, Sussex, declaring she was not born in Sussex. Sophia Cooke was baptised in Loose in 1803 to John and Ann Cooke. No  obvious marriage entry for John and Ann has been identified.
Eliza''s baptism was not in Chartham, because it is a different John and Ann COOK/COOKE.
Eliza's death has not been proven, but is thought to be the North Aylesford registered death in 1848, where the age was declared as 49. Francis WELCH occupation was a woolstapler, and Jacob WELLS a paper maker, who had worked in the Maidstone area, and his family had also been in Maidstone as he travelled around the home conties at various paper Mills. His and his wife Sophia's where abouts at all census entries has been found, and there is no indication of any clue to the COOKE family.
So the question, is whether there is a likely baptism of Eliza COOKE/COOK 1798/9 in Kent, whether there may be additional siblings, and of any John COOKE to Ann marriages.
Questions we have considered, was John COOKE involved in papermaking as well. The proximity of the Maidstone Mills certainly the reason for Sophia's husband being there.
I have been looking at the occurrence of a Maria COOK  bborn circa 1800 marrying a John MORRIS in Goudhurst , as a feasible sibling, They had a daughter Sophia in 1828, her birth place declared as Maidstone in census entries.
We do have 2 DNA links to daughters of Eliza to the WELLS descendants of Sophia .

A William ROBERTS with wife Frances is detailed on a Quaker marriage entry from Norwich on 7th Jul 1761 as the parents of Thomas.
This post is specifically to enquire if there are any records of these ROBERTS, in Mildenhall that might tie up with this record, because Mildenhall is detailed as the abode of Thomas's parents. The information regarding Thomas's family in Norwich is already known. They had at least 6 children all with Quaker birth records, some of them even detailing the midwife. The names of the children might have some relevance when identifying siblings or marriage, they are John, Elizabeth, William, Mary, Susanna, and, Anne.
Thomas married a Susanna BREWER. Thomas was also a wool comber.
Son Thomas's age is unclear, the quaker marriage entry says with the consent of parents, whether this is a standard quaker phrase in their marriage entry is not understood. So he could have been born as late as 1750's, but could be much earlier.
Whether Thomas was born in Suffolk as well,  is unknown. The ROBERTS may have come from anywhere.

I am currently researching the HILDER families in and around  the Kent Sussex Surrey Borderlands 1700 - 1850 .the Sarah HILDER  I am  looking for was born circa 1770,
Married a William FIELDER in Edenbridge 23 rd April 1795.
They have a family of atleast 4 children William 1795, Louisa 1802, Harriet 1805, Charlotte 1808 and suspect and earlier Elizabeth.
There is clearly a fairly wealthy farming family of HILDERS  in this region  with several very useful wills 1795 - 1828.
I have several Sarah HILDERS born in Sussex, but none if them seem likely candidate's. Kent records appear to be a possible source of  information, but nothing positive  has come to light.