Mercedes trackside engineering director Andrew Shovlin has set a target of overhauling a "bruised" Red Bull going into F1's summer break.
The final race before a near four-week hiatus takes place at the Hungaroring, which is expected to suit Red Bull more than Mercedes, even though Hamilton is an eight-time winner at the venue.
Mercedes go into the race just four points adrift of Red Bull following the British Grand Prix in which Max Verstappen crashed out on lap one and Lewis Hamilton claimed his eighth victory, leaving the Briton eight points shy of the Dutchman.
Mercedes' pace at Silverstone was to be expected as it has long been a stronghold for the team, although ahead of Hungary, Shovlin is coy on the team's chances.
"This [Silverstone] is one of our best tracks so it would be naive for us to think we can go there and expect to carry this performance in," added Shovlin.
"Red Bull are going to be good at a high downforce circuit. Frankly, they are good at every circuit at the moment and are going to be a bit bruised from their experience here, so I am sure they are going to come back really strong."
But with Red Bull again firmly in Mercedes' crosshairs, Shovlin added: "We are about halfway through the championship, there are very fine margins in terms of the points and for us, we are going to throw everything at it now to try and get through.
"If we can get ourselves ahead going into the summer break, that would be fantastic. That is probably the target we will set ourselves.
"It is a stretched target but we have shown here that anything is possible, you have just got to keep going and try to get better, try to improve."
Mercedes outlines areas of improvement
Red Bull had won five races in a row prior to the weekend's dramatic events in which 40 points were hacked out of its constructors' championship lead as the only points it scored were the three from Verstappen's win in the inaugural sprint.
Despite the much-needed success, Mercedes knows there remain "a few areas we need to go off and work on", according to Shovlin if it is to continue to take the fight to Red Bull and Verstappen.
"Lewis, we didn't get the launch perfect and Lewis was then a little bit slow on the paddle in the first one but we can certainly work together to improve that in terms of the sprint quali," said Shovlin.
"Probably, the bigger part of Valtteri's [Bottas] issue was struggling to get the tyres up to temperature to attack the lap.
"Again it is a weakness and like all of them, we create a job list after the race on a Sunday and we will be heads down trying to tackle all those various problems."