The 23-year-old, who entered the tournament ranked 114, beat ninth-seed Cobolli 6-4 7-6 (7/4) 6-0 on Centre Court.
Fery is the first British wildcard to reach the semi-finals at a grand slam in the open era, and joins Sir Andy Murray, Tim Henman, Cameron Norrie, and Roger Taylor as home male members of the Wimbledon last-four club. Fery is now the only non-seeded player left in the tournament.
Wildcards are players whose world ranking is not high enough to qualify automatically for The Championships but who are accepted into the main draw by the committee.
Fery’s strong run has been a major upset of the tournament, having only two grand slam victories to his name before Wimbledon.
The Briton has quickly become a crowd favourite and secured his victory on Wednesday in front of nearly 15,000 cheering Centre Court spectators and the Queen, who watched on from the royal box.
He defeated former semi-finalist Grigor Dimitrov after a five-set thriller over nearly four hours to reach the quarter-final, before making quick work of Cobolli, 24, who was the runner-up at last month’s French Open.
Fery’s intensity and strong ball-striking appeared to rattle Cobolli, who struggled to break back against the Briton.
Especially in the third set, Fery was in full control, much to the frustration of his Italian opponent, who often looked exasperated when turning to his coaching team.
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