Bastianini added to his sprint win on Saturday by racing past Martin inside the last two laps to claim victory, while the Spaniard finished second to move back above third-placed Francesco Bagnaia in the overall riders' championship.
Ducati-Pramac's Martin arrived at Silverstone 10 points behind Bagnaia, who won the last four grand prix, but second-placed finishes in the sprint and grand prix meant he leapfrogged the Italian back into the lead.
It was a weekend to forget for Bagnaia after he crashed out of the sprint and then ceded the early lead in the grand prix race.
But his compatriot Bastianini will have fond memories of Silverstone 2024 after producing a stunning late run to sprint to the double.
Bagnaia sprang into the lead from the start but was eventually reeled in on lap 14 by Martin, who had started on the second row.
Bastianini soon caught up with the two pacesetters and, after going past Bagnaia, he made his move on turn three of the 19th lap to fly ahead of Martin and sprint towards the chequered flag.
