His possible baptism:

Name John James Martin
Gender Male
Christening Date 30 Apr 1839
Christening Place Eccles, Lancashire, England
Father's Name Charles William Martin
Fther;s name note: Merchant
Mother's Name Sarah

Ref:
Indexing Project (Batch) Number C01079-3
System Origin England-EASy
GS Film number 1545551
Reference ID item 3 p 56
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1872: Of Belvedere, Christchurch, Hants and co-executor of mother.
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Now for quite a few lines of duff denealogy chasin a read herring, left in for your (the reader’s) amusement and learning - don’t do as I do, do as I say!.

His probable death:

Surname   First name(s)   Age   District   Vol  Page
Deaths Jun 1909   (>99%)
MARTIN John James 70 Pancras 1b 67
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But his probate refers to him as normally known as James.  And this death regisgtration and location looks more like his:

Surname   First name(s)   Age   District   Vol  Page
Deaths Mar 1910   (>99%)
Martin James 70 Steyning 2b 200
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In the probate entry his widow is written as:
  “Emma Maria Martin widow”
I have searched through all the marriages of James Martin from 1860 to 1895 with any Emma and only this appears with an Emma Maria:

Surname   First name(s)      District   Vol  Page
Marriages Jun 1893   (>99%)
Bowden Emma Maria Bethnal Green 1c 419
Butler Rebecca    Bethnal Green 1c 419
MARTIN James    Bethnal Green 1c 419
Worley Edwin William J    Bethnal Green 1c 419

This cannot be identified as in the census of 1901 he was with his sister Sarah Amelia (Emily) and by 1911 he was dead.

Of course it could be that this James Martin married Rebecca Butler.

There are quite a few other methods of determining his wife:

1. Go through all the censuses of James Martin born in 1839 +/- 1 year.

2. Find Emma Maria Martin’s own death and get the birth certificate which will provide her maiden name.

3. Possibly look through a few newpaper BMD notices (he was a wealthy man).
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Taking the first one first, there are about 25 Emma M Martin deaths on FreeBMD between 1909 and 1950.  None were in Sussex, but it is not uncommon for widows to move after a bereavement, if only to get near their own relatives.
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She might have remarried.  There are about 15 of these, of which 2 were in Kent and none in Sussex.
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There are no censuses for a James Martin born in 1839 and with an Emma Martin in the same house.  Though John J Martin is in the 1901 census with his sister ‘Amelia S Amphlett’.

He was born in Lancashire.  There are several censuses for a John J Martin born in 1839 in Lancashire.

One is a retired Commander of the Royal Navy living in Axminster, Devon with wife Margaret E Martin and two children.  This couyld be interesting as his elder brother George E Martin was listed as a Naval Cadet in the 1851 census.

And with two earlier children, they are also to be found in the 1881 census.

But the marriage of John J Martin and a Margaret E ? cannot be found.

Now to search censuses for a John J Martin born in Lancashire in 1839.  This produced four censuses at the top of the list; the first and fourth, 1851 and 1901 were definitely him; it looks like the other two, 1881 and 1891 were also him:

Last name First name Born Died Event Location   
Martin John J 1839 — 1851 1851  Milton, Lymington, Hampshire
Martin John J 1839 — 1881 1881  Axminster, Devon
Martin John J 1839 — 1891 1891  Axminster, Devon
Martin John J 1839 — 1901 1901  Tonbridge Wells, Tonbridge, Kent

All four had births in 1839 for him in Manchester, Lancashire and the first said also Pendleton.

It is looking very likely that the second and third were him also and that his wife was Margaret E and not the Emma Maria I had identified earlier from the probate records.

Now to see if I can find a death in Devon for him and with the name John J(ames) Martin.

This produces a death in Devon of:

Surname   First name(s)   Age   District   Vol  Page
Deaths Dec 1923   (>99%)
Martin John J 85 Newton A. 5b 126

And the will (see Will Notes) includes an apparent relation, in fact his son (see 1911 census) who is in the RN, continuing an apparent family tradition and, the killer, one of the executors was also executor for his sister Sarah ‘Amelia’ Holme.  Definitely Bingo!
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Reverting to sanity, his census entries for 1881 and 1891 are:

1881:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year Occupation Birth place

John J Martin Head Married Male 42 1839  Retd Commander R N  Manchester, Lancashire
Margaret E Martin Wife Married Female 35 1846  -  Netherbury, Dorset
Margaret E Martin Daughter Single Female 2  1879  Scholar  Sherborne, Dorset
Eva L Martin Daughter Single Female 1 1880  -  Somerset, England
Sarah J Baker Servant Single Female 20 1861  Housemaid (Dom Serv)  Devon
Susan A Baker Servant Single Female 24 1857  Cook (Dom Serv)  Stockland, Devon
Alice Tozer Servant Single Female 18 1863  Nurse (Dom Serv)  Devon

Census details
First name(s) John J
Last name Martin
Relationship Head
Marital status Married
Gender Male
Age 42
Birth year 1839
Occupation Retd Commander R N
Birth town Manchester
Birth town as transcribed MANCHESTER
Birth county Lancashire
Birth county as transcribed LANCASHIRE
Birth place England
House name Coombfield
Street -
Town -
Parish Axminster
County Devon
Country England
Registration district Axminster
Archive reference RG11
Piece number 2127
Folio 8
Page 10
Record set 1881 England, Wales & Scotland Census
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1891:  The two elder daughters were away from home:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year Occupation Birth place

John J Martin Head Married Male 52 1839  Retired Commander Royal Navy Manchester, Lancashire
Margaret E Martin Wife Married Female 45 1846  -  Netherbury,  Dorset
George F Martin Son Single Male 6 1885  Scholar  Axminster, Devon
Kathleen M Martin Daughter - Female 4 1887  Scholar  Axminster, Devon
Elizabeth Peach Servant Single Female 22 1869  Cook Domestic Servant Musbury, Devon
Anne Harris Servant Single Female 22 1869  Nurse Domestic Servant  Stockland, Devon
Elizabeth Lockyer Servant Single Female 22 1869  Nurse Domestic  Servant Branscombe, Devon
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In 1901 he was with his sister and three of the children were away, leaving only his wife and daughter Eva:

First name(s) Last name Relationship Marital status  Gender  Age  Birth year Occupation Birth place

Margaret Martin Wife Married Female 55 1846  Own Means  Netherbury, Dorset
Eva Martin Daughter Single Female 21 1880  -  Middle Chinnock, Somerset
Agnes Passmore Servant Single Female 26 1875  Cook (Domestic)  Exeter, Devon
Florence Wilton Servant Single Female 21 1880  Housemaid (Domestic) Bigbury, Devon
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In 1911 three spinster daughters were still with them, his son George was entered but erased as he wasn’t there(!) and for his wife he put down that they had had four children all of whom were alive:

First name(s) Last name Relationship Marital status  Sex  Occupation Age Birth year Birth place

John Martin Head Married Male Retired Commander R N  72  1839  Manchester Lancs
Margaret Martin Wife Married Female - 65  1846  Netherbury Dorset
Margaret Martin Daughter Single Female -  32  1879  Sherborne Dorset
Eva Martin Daughter Single Female - 30 1881  M Chinnock Somert
May Martin Daughter Single Female - 25 1886  Oxminster Devon
Alice Manley Servant Single Female Cook Domestic  27  1884  Luppitt Devon
Florence Turner Servant Single Female Housemaid Domestic  20  1891  Teignmouth Devon
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This probate of 8th December 1923 is more believable:

MARTIN John James of 7 Barton crescent Dawlish Devonshire died 4 November 1923  Probate London 8 December to George Frederick Martin Paymaster Commander RN Kathleen May Hearle (wife of Nathaniel Salmon Hearle) and the said Nathaniel Salmon Hearle solicitor,  Effects £6441 14s 9d.

The confirmation that this is him is that his sister Sarah ‘Amelia’ Holme had the same executor of Kathleen May Hearle (wife of Nathaniel Salmon Hearle).  Bingo!

Not merely this, but Katherine May Hearle was his daughter!
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Previously I had thought this might be his probate:

Possibly this is his probate but he was definitely baptised as ‘John James’:

MARTIN James otherwise John James of 27 First Avenue Hove Sussex died 27 November 1909 Probate Lindon 6 January [1910] to Emma Maria Martin widow and Charles Lynn gentleman.
Effects £66382 3s 3d.  Resworn £69201 5s 9d.
and £68800-9-2.
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In the 1911 census they said they had been married for 43 years, which means that their union started c. 1878.

But no marriage found in any of FamilySearch, FreeBMD or FindMyPast.