He was born circa 1849 in Lockwood, the son of cloth finisher James Shaw and his wife Harriet.
The 1861 Census lists 12-year-old John Edward working as an errand boy, living with his family on Bradford Road, Fartown.
By 1871, the family had moved to High Street in central Huddersfield, where James Shaw worked as a chapel keeper. By then, John Edward was working as a woollen warehouseman.
He married Martha Robinson in the early 1870s and they had a total of ten children, although the identify of three remains uncertain:
By around 1877, he was residing at 6 South Parade, where he had established a photographic studio. Prior to that, it is believed he was based at 26 Manchester Road, Huddersfield.
In November 1883, he gave a lecture on the topic of "Recollections of a recent tour in Switzerland and Savoy" at the High Street Methodist New Connexion Sunday School. With the aid of a triple oxy-hydrogen lantern and his photographs, he described his journey from London to Switzerland via Paris. 
Other lectures illustrated with projected photographs included "Reminiscences of a spring tour in Italy" (November 1884), "Easter trip to Rome" (February 1885) and "Fjords and Fosses, or what I saw in Norway" (March 1888).
In 1887, the family moved to the newly-built Burlington House on Park Drive, near Greenhead Park, where he set up a new studio.
In December 1887, the Huddersfield Chronicle listed Christmas preparations in the town, along with suggestions for seasonal purchases:
Photographs, portraits, &c., which are in demand all the year round, are much wanted for Christmas. In his new studio at at Burlington House, Park Drive, Mr. John Edward Shaw is prepared for emergencies, and visitors may be assured not only of good accommodation, but also of every effort being made to give them satisfaction.
The following Christmas the following was printing in the Chronicle:
Fancy Dress — Mr. John Edward Shaw, Burlington House, has every convenience for taking photographs in fancy or evening dress during the festive season. His studio, reception, and dressing-rooms are warmed through with hot water apparatus. Perfectly clear and uninterrupted light.
In January 1893, he exhibited a pair of "enlarged photographs" of Mr. and Mrs. Thomas of Liverpool measuring 48 by 38 inches, which were "of permanent carbon, finished in monochrome [...] and very artistically finished."
Shaw was admitted as a Fellow of the Royal Photographic Society in the 1895.
In May 1899, he advertised his imminent return to Huddersfield from Sheffield:
To my Customers
Ladies and Gentlemen, having transferred to my son, Charles Raven Shaw, the Business carried on during the past few years at Kensington House, Sheffield, I am now able to devote the whole of my attention to my Huddersfield Studio. Personal attendance daily from 10 a.m. to 5 p.m. Pearlatype Matte Surface Photographs and Circular Medallions are taking the lead this season.Yours faithfully, JOHN EDWARD SHAW.
John Edward Shaw died on 3 September 1916, aged 67, following a severe illness. He left an estate valued at £855 14s 9d. His obituary article noted his six-decade long association with the High Street Methodist New Connection Chapel, where he had been a trustee, a church secretary (for 25 years), and also a Sunday School teacher. He had also been the vice-president of the Huddersfield Temperance Society, a founding member of the local branch of the Y.M.C.A., and a Freemason Chaplain to the Huddersfield Lodge. It was reported that his son would carry on the business, entering into a partnership with another local photographer named Wilkinson.
In March 1917, adverts appeared in the local press announcing that the business was to be discontinued and the leasehold on Burlington House was offered for sale. Patrons were advised that they had two months to order any "photographs or enlargements from negatives taken during the last thirty years."
On the morning of 19 December 1917, the body of Charles Raven Shaw was found hanging in the studio of Burlington House. It was reported he "had been somewhat strange in manner during the last few weeks". At the time of his death, he had been lodging at 27 Trinity Street and on the evening before had left saying he needed to "blow the cobwebs off". When he failed to return, the police were informed and his business partner Mr. Wilkinson went to Burlington House, where he discovered the body.
Frank Hubert Shaw went on to become a writer of fiction, which included The Wonderful Adventures of Captain Smith of the Astonian Navy (1906), The Swoop of the Eagle: A Great Story of the Motherland's Dire Peril (1914), Secret of the Sargasso Sea (1920) and Outlaws of the Air (1927). An autobiography titled Seas of Memory was published in 1958, prior to his death in October 1960.