After setting the second fastest time in Friday's practice, Lewis Hamilton said he had a good day.
He was 0.186 seconds slower than the pace-setting Carlos Sainz's Ferrari.
A number of aerodynamic upgrades have been introduced by Mercedes.
The team made an improvement, according to Hamilton.
He said that the car's major problem wasbouncing through the high-speed corners.
The seven-time champ said it was bouncing. Not necessarily on the straights, but through the corners it's pretty harsh, not physically, but in the car on the tires and everything.
It feels like a small step forward.
George Russell had a hard time getting the best out of his car in the first part of the race.
The times aren't likely to reflect true competitiveness because Charles Leclerc, who has six pole positions in nine races this year, didn't set a time on his simulation run.
On the first runs of the session, Leclerc was the fastest, but he barely improved on the softer tires.
Leclerc was ahead of Alonso.
In the race, Hamilton set an average pace that was more or less an exact match for Leclerc's on the same medium tires.
Andrew Shovlin, Mercedes head of trackside engineering, said that it looks like they have made a step forward.
The long-run pace was encouraging and I think there will be more to come from Red Bull.
We usually see a half a second gap on a long run, but it didn't seem like it was there.
The circuit might suit the car. The update pushed us in the right direction, but there is a lot of work to be done.
Verstappen complained his rubber wore out after just two laps after Red Bull and Sainz ran the soft tyre.
Red Bull'sSergio Perez was seventh fastest, ahead of Russell, Daniel Ricciardo, and Lance Stroll.
"I'm happy the car seems to be in a decent place, it's a little better than we were expecting," he said.
Significant technical developments have been introduced by Mercedes as they try to improve their performance
The W13 car has been revised extensively by the world champion team in order to limit the "bouncing" that has afflicted the car so far this season.
The track characteristics at Silverstone were supposed to help Mercedes make up some ground. The surface is smooth, which should limit bouncing, and there are few slow corners to make up for the car's other weakness.
Red Bull and Ferrari have new engine covers that aim to improve airflow to the rear and increase down force.
Red Bull have not given a clue as to what is causing the noise from the car.
Williams, the slowest team on the grid, have the biggest upgrade, with Red Bull-inspired sidepods.
The only Williams driver with the new parts was Alex Albon.