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Yes there are living descendants.  A son of one of the great uncles and a daughter of the other great uncle.  I am not sure how I would go asking them to take a test.  I understand this would be a good way to help work things out.  I recently emailed both of them as I touch base with them every so often and update on births and deaths in my family and any other family history information.  They both live in England and I live in Australia.  I did tell them about my husband's recent discovery of a half brother through an Ancestry DNA test, something that was a huge surprise for him.  There was no intention of asking them to do a test, simply to let them know of something quite remarkable that happened with my husband's family, a situation that has been extremely positive on both sides. One has replied to my email and nothing was mentioned about DNA, the other has not replied to my email.  Not sure if he still has the same email, perhaps he may be not well.

I do know that the 154 cM match, his mother Mary does not know who her father was.  Mary and all of my father's family lived in close proximity to one another.  Mary's birth certificate gives a father's name but this is not her real father according to her son.  In the 1911 Census, the father named on the birth certificate was living at an address where my grandfather and my great uncle were living.

It is possible that my grandfather does have a half brother and I do not know about this yet.  Anything is possible.

Regards Kaybron

Thank you for the responses Craclyn, Gadget and davidft.

My grandfather was born in 1898 and his last child with my grandmother was in 1939.  My father was born in 1920.  Mary, the mother of my 154 cM match was born in 1931.  My grandfather has 2 possible brothers that could be Mary's father. 

I am of a similar age to the person I match with.

Kaybron

One of my top matches is 154 cM.  The person I match with does not have many people in his tree but I have been in touch with the person who manages his tree. From our shared matches I have established that we must be connected through my father, not my mother.  My father's family largely lived in the Croydon, Surrey area and this person's mother (I shall call Mary) was also born in the Croydon, Surrey area.  Through contact with the tree manager I have been told Mary does not know who her father is. I have looked at the DNA Painter tool and think my 154 cM match could be a half second cousin.  If he is a half second cousin, what common ancestor would we have.   
 

I do not know who my grandmother's parents are and am hoping that through DNA I am able to gather some possible leads.  I have sent emails to my top matches and have not received replies.  One I am particularly interested in is a Jon Spong with 149cM.  We have a number of shared matches and I am not able to work out connections with any of them.

I am a little bit annoyed as my husband who does not really share my interest in family history was recently asked to do a DNA test through Ancestry.  He agreed and as a result discovered a half-brother.  His half-brother (Rob) had been trying to find out for 40+ years who his father was.  He was given a DNA kit and eventually sent this away.  A second cousin of my husband was also given a kit as a birthday present and when his results came through he was a match for Rob.  He contacted Rob as he did not know how they were related and after discovering that Rob did not know who his father was he agreed to help him.  This eventually led to Rob contacting my husband and asking him to complete a DNA test.  cMs came back as 1,754.   My husband received further emails from a person who had a DNA test several years ago and was hoping to find out who her great great grandfather was.  She had managed to find out who her great great grandmother was through DNA but was waiting for someone like my husband to pop up and she would be able to work out who her gggrandfather was through shared matches and his family background and movements.  Her gggrandfather was a brother to my husband's gggrandmother.  They both came to South Australia in the 1860's from Germany.  My husband's gggrandmother stayed in SA but her brother moved to Queensland where he had a relationship and fathered a child.

I am hoping that down the track I have some luck.  I have recently asked a cousin in the UK if she would be willing to send away a DNA sample so I can used shared matches to further my research.