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Wow  That's him, thanks very much,,, so he died on Wednesday 24th dec 1755 on Christmas eve.

I have 3x burials on my list for a John Harmer in 1755:
burial 17-11-1755 St. Margret's, Westminster, London.
burial 21-12-1755, St. Andrews, Norwich, Norfolk.
burial 20-01-1755, Southrepps, Norfolk 

Maybe
Will of Elizabeth Rippingall, Widow of Norwich , Norfolk
26 May 1743
https://discovery.nationalarchives.gov.uk/details/r/D509293

Haven't read it, but her granddaughter Elizabeth is certainly in there.

Looking at the will which is/was difficult to read, have managed to glean the following:
Elizabeth Rippingall, Widow of Norwich, Norfolk, 26th May 1743 (so Rippingall and not Rippingale)
To be buried at St. Andrew, Norwich, Norfolk as where her parents (It does go on about St Mary's  somewhere in the County of Norfolk, but I cant make anything of it)
Elizabeth Rippingall her granddaughter seems to inherit everything. Ann Rippingall her other granddaughter is also mentioned.
There is mention of her son: John Rippingall, who I am assuming the father to Elizabeth and Ann.
The only other mention of note is of a Thomas Brown of Elling, Norfolk (Elling = Ellingham?) I cant work out in what context he is mentioned.

So looking for a John Rippingall with mothers name of Elizabeth (which should give the fathers name) and the a marriage of John Rippingall bearing children Elizabeth and Ann (which should give the mothers name) 

but, as they say ' All the best laid plans of mice and men,,,,' 

On googlebooks I came across the 'History, Gazetteer and Directory of Suffolk, and the Towns- Page 407'  the mention of John Harmer, druggist at Wrentham in Suffolk, this is the same place as mentioned on the baptism of:

i. Elizabeth Rogers, bap 19-05-1751, Old Meeting (Independent) Norwich,
parents Joseph and Elizabeth Rogers of Wrentham.

Were Joseph Rogers and John Harmer working together back in 1751 at Wrentham, Suffolk? Still trying to work out the significance of this link

jonwarrn, I think you are defiantly on the right track and that John Harmer plays a large part in this story ! 
(I hope the link below works)

https://www.google.nl/books/edition/History_Gazetteer_and_Directory_of_Suffo/ZgxIAAAAMAAJ?hl=en&gbpv=1&dq=John+Harmer+surgeon+Norwich&pg=PA407&printsec=frontcover

dear all,
thanks for your efforts and all the information, I shall work my way through everything 

@ ColC
I have now also checked for other possible offspring of Joseph and Elizabeth:
i. Elizabeth Rogers, bap 19-05-1751, Old Meeting (Independent) Norwich
ii. Katherine Rogers, bap 16-08-1752, St Andrew, Norwich
iii. John Rogers, bap 05-11-1753, St Andrew, Norwich
iv. Richard Rogers, bap 08-10-1754, St Andrew, Norwich
v. Diana Anna Rogers, bap 30-11-1755, St Giles, Norwich
vi. Joseph Rogers, bap 16-01-1756/7, St Giles, Norwich
vii. Susanna Elizabeth Rogers, bap 27-08-1760, St Andrew, Norwich
  ( Susanna Elizabeth Rogers, burial 30-08-1760, St Andrew, Norwich)

i. Curious that the baptism takes place in an Old meeting house (Independent) .The actual baptism entry reads: ' Elizabeth daughter of Joseph and Elizabeth Rogers (of Wrentham) bap 19-05-1753. Wrentham being just accoss the border in Suffolk 

v and vi. Not so sure, why the sudden move to another Church? St. Anrew doesnt look very far from St. Giles.

vii. I believe that Susanna and Elizabeth are one daughter with a double name, at least it looks that way on the actual baptism register with what looks like an Elizabeth being added between and above Susanna Rogers with an upside down v below between and below.

@ jonwarrn
I like the 'John Harmer' name change theory. I have been nursing the idea that maybe Harmer Rogers was adopted and had something to do with the departed John Harmer, but was not very far with that. Anyway, as you say, the clue would be to see if 'John Harmer' is accounted for ! As of yet I have not looked at any of the other possible offspring of Joseph and Elizabeth, excepting Susanna Elizabeth, who didnt live for long.
Think I need to look at John Harmers family and try to put that together too 

@Paco
Thanks for the Dusty Docs reference, I do not know this site and hope to make good use of it in the future once I get the hang of it 

@amondg
I had searched for Elizabeth Quintin or Quinton and had found only 2 candidates:
i. Elizabeth Quintin: parents Thomas and Margaret, baptised 29-01-1748, St Stephen, Norwich
ii. Elizabeth Quinton: parents John and Mary, baptised 15-09-1751, St Benedict, Norwich
burial Elizabeth Quinton, 25-08-1751? St Benedict, Norfolk 
This was a far as I got, so the burial of ' Elizabeth Rogers nee Quinton is buried 17 February 1803 at Woodford age 49  -born circa 1755'  Is something worth looking into with regard her origins 

done some further work on the 'Cross sisters' theory:

On searching for every Catherine and Mary Cross (1680 - 1700) there were only one Catherine and Mary with parents of the same name:

Catherine Cross bap 10-06-1679, St. Martin in the Fields, Westminster, London
parents: William Cross and Catherine.
Mary Cross bap 03-04-1683, St. Martin in the Fields, Westminster, London
parents: William Cross and Catherine.

I am assuming that both girls would not be married before the age of 18, thus:
Catherine married in 1717 was born before 1699
Mary married in 1724 was born before 1706

William Cross and Catherine must have married outside London as there are no immediate candidates.

This also kinda disproves my previous post:
'at St Dunston and All Saints, Stepney, London. Burial 30-05-1751,
Mary wife of Joseph,  aged 49 (= b c1702)' 

Will now search for Marys born 1700-1706 in London