He was briefly dislodged from top spot by home hero Cal Crutchlow (LCR Honda), though Marquez would soon move the goalposts further with the first sub-two minute lap of the day, a 1m59.972s.
Marquez bettered this after 10 minutes to a 1m59.743s, though was once again deposed by Crutchlow, who was the first of the frontrunners to put in a time attack on fresh soft rubber.
Crutchlow’s 1m59.184s, the fastest time of the weekend so far and the fastest-ever lap of Silverstone on a MotoGP bike, gave him an advantage of 0.559s over the field.
However, Friday pacesetter Quartararo soon fired in the first sub-1m59s lap at the circuit, moving 0.283s clear of Crutchlow with a 1m58.901s – which the Petronas SRT rider improved next time around to a 1m58.727s.
This came under minimal threat for most of the remainder of the session, though Rossi on the works Yamaha started to light up the timing screens in the closing moments.
The Italian briefly went top with a 1m58.693s, but Quartararo denied him at the death by 0.146s with a 1m58.547s, the new lap record.
Marquez moved back up to third late on, though some 0.366s off the pace, ahead of Pramac’s Jack Miller – who was forced to abandon one of his GP19s after it developed a technical issue on the run to Stowe 25 minutes into the session.
Ducati’s Danilo Petrucci was fifth fastest to book a spot in Q2, but teammate Dovizioso was unable to do the same and ended the session just over a tenth outside of the top 10 in 14th.
Crutchlow headed the sister Yamaha of Maverick Vinales, with the second Petronas bike of Franco Morbidelli, LCR’s Takaaki Nakagami and Aprilia’s Aleix Espargaro – who will make his first Q2 appearance since May’s French GP – completing the top 10.
Alex Rins will face the first qualifying segment alongside Dovizioso this afternoon, after the Suzuki rider missed out on a place by just 0.011s.
Jorge Lorenzo’s difficult return to action continued this morning, with the Honda rider failing to improve on 21st and only finding four tenths of laptime over his best Friday effort.