I see the advertisement at the link you have posted.
You might reasonably assume that the advertisement appears in a publication, not necessarily a newspaper, dated 25 April 1954.
The name and location of the publication is unknown.
It is unknown if this advertisement appeared in any other publication in 1954....or ever.
If you have reason to believe that Florence Evelyn SUMNER, died 1952, left an estate, you might suspect that the enquiry possibly relates to her death.
If Florence Evelyn SUMNER left no estate then the notice in the publication might not be a consequence of her death, 1952.
The notice in an unknown publication would seem to be relevant to a legal matter being handled by
Walter BURGIS and Co.
If you could see, by means of notices in publications, how extensively Oliver Herbert SUMNER was being sought, it might suggest..... why..... he was being sought....and where he ever lived.
One notice for an 85 year old man, last heard of 58 years earlier, might suggest that is all that is legally required for the matter. ....one notice.
I think the notice in the publication is not related to the death of Florence Evelyn SUMNER, 1952.
If it is about SUMNERs, but not Florence or the children born of the marriage. it might be useful to know what is happening in the lives of Oliver Herbert's SUMNER family in 1953 - 1954.
Is he....... named or ultimately...a beneficiary in a SUMNER estate?.
Using Ancestry Probate Calendar....I do not see Florence Evelyn SUMNER, died 1952.
Using Britishnewspaperarchives...I do not see the Solicitor's notice naming Oliver Herbert SUMNER.
How did Florence Evelyn SUMNER support her family when her husband, Oliver Herbert SUMNER left his wife and children?