I followed up on all of the information on Dr. Brogdon's life and found no mention of adult Adele other than on their marriage in the South Shields area. He was born 1899 - Hexham area. His death was registered in the Ulverston Registration District which includes Coniston. The only thing I can suggest is checking the Electoral Registers for British West Hartlepool for the "Brougham Terrace" address mentioned below - 1928 and onwards for her (but possibly earlier according to her qualifications to vote) and then to 1932 and possibly later than that if she was with him in Brougham Terrace. The BIG IF! I found no children born to the couple.
The article gives more concise details of the accident.
West Cumberland Times, Wed. April 13, 1932
DOCTOR KILLED AND TWO INJURED.
_____
CONISTON TRAGEDY.
A doctor - one of a party of three experienced climbers, was killed, and
his woman and male companions were injured badly when their rope broke on
Sunday evening, on the 175ft Dow Crag, near Coniston, they had crashed into a
precipice.
The dead man was Dr. John Stratton BROGDON, age 32, radiologist at
Hartlepool Hospital, of Brougham Terrace, Hartlepool.
The injured are Miss. Vera BROWN, aged 37, French mistress at Tottenham
County School, of Baronet-road, Tottenham, N.
Mr. H. W. TILMAN, aged 34, coffee planter in Kenya, on a visit to his
parents at Grove-road, Wallasey, Cheshire.
While a strong wind and a blinding rain were sweeping the mountain, the
party were climbing Easter Gully, one of the five gullies on Dow Crag,
forming part of the range of hills that include Wetherlam and Coniston Old Man.
Their rope broke and the three crashed into the precipice.
Dr. BROGDON, who was apparently killed instantly, and Miss. BROWN fell
on a ledge, and Mr. TILMAN, lay unconscious for some time. He was the least
seriously injured, and he managed to struggle for four hours in the dark to
Coniston - a journey of four miles, normally taking an hour or so - for help.
Local climbers, police and villagers with lanterns and ropes started out
searching the mountain side in the gale to find Miss. BROWN and the doctor's
body.
When the rescue party reached the crag, Mr. J. C. APPLEYARD, secretary
of the Fell and Rock Climbing Club, made a perilous ascent in darkness. He
drew up improvised stretchers and let down the body of Dr. BROGDON and then the
injured woman.
The walk back to the village across the mountain side was covered in a
howling gale, and was not ended until early on Monday morning.
Mr. TILMAN and Miss. BROWN were both too badly injured to attend the
inquest, which was formally opened at Coniston on Monday afternoon and then
adjourned.