Fery, a wild-card entry, won their marathon round three clash after more than four and a half hours – 2-6, 7-5, 2-6, 7-6, 7-6.
The British number three will next play either Bulgarian Grigor Dimitrov or Italy’s Matteo Berrettini.
Meanwhile, Serena Williams’ comeback at Wimbledon this year is over, after she withdrew from the women’s doubles where she was due to compete alongside her older sister, Venus.
The former champion, 44, said she was “heartbroken” to quit the doubles event due to a knee injury which she suffered during her first-round loss to Maya Joint in the singles event earlier this week.
The Australian, 20, won the match in three sets 6-3, 6-7, 6-3 against Serena who was competing in her first professional singles match in nearly four years.
US tennis star Serena had received a wild-card entry to play alongside Venus, but tweaked her knee in Tuesday’s match at Wimbledon.
The 23-time grand slam champion said on Instagram: “I’m heartbroken to have to withdraw from doubles.
“Coming back to compete again has been a gift, and the opportunity to play alongside Venus once more meant the world to me. I did everything I could but unfortunately my knee just isn’t ready to compete.”
Williams also shared footage of her limping in a heavy bandage, as well as syringes full of fluid, as she confirmed her withdrawal from the competition.
But she left the door open to possibly competing again elsewhere when she added: “All I can say is stay tuned to a city near you.”
The sisters, who won the women’s doubles at Wimbledon six times, including most recently in 2016, had been scheduled to take on Argentina’s Solana Sierra and Colombia’s Camila Osorio at the All England Club.
Tournament director Jamie Baker said the first-round doubles match was pushed back to give Serena “as much time” as possible to recover.
All other first-round matches in the draw were played on Thursday and Friday.
Venus, 46, and Serena last played doubles at the 2022 US Open, losing in the first round to Linda Noskova and Lucie Hradecka of the Czech Republic.
Serena has won the women’s singles at Wimbledon seven times.
Read more from Sky News:
Week-long health warning comes into effect
Prince Harry won’t bring family to London
Meanwhile, defending singles champion and Polish third seed Iga Swiatek, 25, lost in the third round to Alex Eala from the Philippines.
The rising star, seeded 29, won the match 7-6, 6-2 to make it through to the second week of Wimbledon.
Eala, who is aged 21, said: “Maybe for someone like Iga, who has won so many Grand Slams, or maybe someone like Serena or Venus Williams, this achievement may seem small.
“But for someone who grew up in the Philippines… I went to training with my brother and my grandfather every day after school with my ruffled socks and my light-up shoes and chubby cheeks, so… to her, this is everything.
“But because I’m emotional does not mean I’m satisfied, so yeah, okay, next round. Let’s go.”
Eala has set up a fourth-round clash with 2024 runner-up Jasmine Paolini from Italy.
