In May of 1881, 15-year-old H. G. Wells was an apprentice at Hyde’s Drapery Emporium in Southsea (Portsmouth). It was a large, popular shop at 9 Kings Road, a place for men to get good clothes and other necessities. Wells was miserable there, living in the basement with other indentured lads and doing duties he was completely unsuited for. His experience there was the source of his novel Kipps.
In June of the following year, a 23-year-old named Arthur Conan Doyle arrived in Portsmouth, looking to set up a medical practice. He did so at No.1 Bush Villas, Elm Grove, in Southsea. He had tried to make his way in Plymouth, but according to this fell out with his partner, and came to Southsea with little money and no connections.
Kings Road, where the Drapery Emporium was, turns into Elm Grove as you walk along — they are two branches of the same street. Southsea was not that large in the 1880s. As Doyle’s practice expanded, it is very likely he would have required clothing suiting his station, and thus it is entirely possible he would have met the young clerk at Hyde’s.
In the summer of the following year, Wells finally convinced his mother to let him abandon the apprenticeship and left town, while Doyle remained and became active in public life there.
There is no evidence that Wells and Doyle met in Southsea, and neither mentions having done so to my knowledge. That isn’t surprising since neither was much of anybody yet. Doyle was spending his frequently unoccupied time writing stories.
They did meet later, and even were members together on the Allahakbarries, a literary cricket team founded by J.M. Barrie (author of Peter Pan) in 1890 that wasn’t very good but contained people like G. K. Chesterton and P. G. Wodehouse, and other authors who liked using their initials. (Wells was a member but refused to play, which is odd since his father was a famous bowler.)
On a sideline, it was reading J.M. Barrie’s book When a Man’s Single (1888) that inspired Wells to stop writing articles about science teaching and instead write fiction stories for money.
On another sideline, A. A. Milne was also on the Allahakbarries cricket team. He was the son of J.V. Milne, who had run Henley House School and had employed H. G. Wells as science master in 1889. A. A. Milne was one of Wells’s pupils.