The marriage you refer to in Newington to Martha Mepham is also what I have seen but on Findmypast it also states an option of Mary Clark.
I looked, it gives 4 options for a spouse as the GRO indexed 4 marriages on that page and at that time they did not cross reference the bride and groom, so we (and Find My Past) don't know which of the 4 was the bride of John Partis.
The options were: Mary Clark, Martha Mepham, Susan Trim, Hannah Sells
I have access to the parish marriage registers and checked them
St Mary Newington
page 108, entry 216 John Walton married Susan Trim
page 109, entry 217 John Partis married Martha Mephampage 109, emtry 218 George Butchard married Mary Clark
page 110, entry 219 George Batchelor married Hannah Sells
The entry for John Partis says he was of full age a Bachelor, occupation pastry cook and his Dad was John Partis a shipwright. Those details for his father do not match with the baptism record you have and say you are sure about.
re-cap of info given already in this thread:
John Waldron Partis married a Mary Alderton Q4 1841 St Pancras vol 1 page 271
The image for that marriage in the parish register is here:
https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSFH-QSBF-S?i=199&cat=135902you need to sign into family search (its free to create and use an account) to see the image
That entry says that John Waldren Partis was of full age, a bachelor, ocupation painter, f
ather Richard, a butcher.and those father's details DO match with the baptism record.
1851 census Piece 1496, folio30, page52 (indexed on FindMyPast as PARTES)
John Partis Head married age 37, occ Painter ,born
NORTHUMBERLANDMary Ann wife 32 born B*nstead, Hampshire
Mary Ann daughter, age 8
John son age 7
Mary daughter age 5
Emma daughter age 2
Ellen daughter age 0
1861 census (indexed on FindMyPast as PARKIS)
RG09/96 f122 p76 - St Pancras
John Waldson Partis 47 occ Painter bn
Morpeth, NorthumberlandMary 46 bn Hampshire
Mary A 18
Williams T 9
Henry J 7
George F 2
1871 census Piece 203 folio 43 page 78
John Partis Head, 57, occ House Painter, born
Morpeth, NorthumberlandMary wife 52, born Binsted Hampshire
William son, 19 occ painter's labourer
George, son 12, scholar
https://www.gro.gov.uk/gro/content/ - need to sign up for a free account to search
This site gives mother's maiden names for births and ages at death for all years
1842 Q3 St Pancras Mary Ann PARTIS mmn ALDERTON
1844 Q1 Stepney John Richard PARTIS mmn ALDERTON
1845 Q3 St Pancras Maria Elizabeth PARTIS mmn ALDERTON - died Q2 1853- St Pancras, age 8
1848 Q3 St Pancras Emma Grace PARTIS mmn ALDERTON - died Q1 1856 St Pancras, age 7
1850 Q3 St Pancras Ellen Jane PARTIS mmn ALDERTON - died Q1 1856 St Pancras, age 5
1852 Q1 St Pancras William Thomas PARTIS mmn ALDERTON
1853 Q4 St Pancras Henry Joseph PARTIS mmn ALDERTON - died Q2 1866 St Pancras aged 13
1859 Q1 Pancras George Frederick PARTIS mmn ALDERTON
John Waldron Partis died Q3 1871 St Pancras aged 57, burial 07 Aug 1871, Camden
in 1863 Mary Ann Partis married Robert Cambridge Woodard at Trinity Church Marylebone, her father was recorded as John Waldron Partis, a painter. He was a witness and signed John W Partis
According to William Thomas Partis' marriage record to Ann Elizabeth Turner in 1887, Lincoln St Swithin his dad was, as you say, John Richard Partis
a painter. Please bear in mind you don't know WHO gave the info, and whoever did may have thought as he had a brother called John Richard that his Dad was also John Richard - or it may have been given as John Waldron when they first went along to arrange for the banns to be read, the vicar, as they did, scribbled the info on a piece of paper and misread it when he wrote out the register in advance ready for them to sign . I've seen odder errors. In later census years William Thomas is shown as being born in 1852, London which is either a good match for the above census returns and birth reg or a big co-incidence.
Given all the above, I really think that on balance this is the family you are looking for. The chances of another John Partis, who was born c1813 in Morpeth, Dad Richard, a butcher ending up in London are slim. I can't explain the sudden appearance of a middle name Waldren but the rest of the evidence has enough checking points on birthplaces and ages to make it all highly likely.
Only you can decide though, its not my family :-)
Boo