Hamilton has ruled the roost at his home event, winning six of the last eight races staged at the Northamptonshire circuit.
But the seven-time world champion will arrive for the 10th round of a scheduled 23, trailing Verstappen by 32 points and without a victory in his last five appearances.
The momentum is in Verstappen’s Red Bull camp and Hamilton expects his rival’s dominance to continue.
Asked if a planned Mercedes upgrade for the Silverstone round can provide him with hope, 36-year-old Hamilton confirmed his fears: “Not really. It is definitely not going to make up the time.
“There is a long way to go but we cannot match Red Bull at the moment. We will do our best but it is definitely going to be tough.”
Hamilton led Verstappen by 14 points after the fourth round of the season in Spain on May 9 – the scene of the Briton’s last triumph – but the Dutchman is now firmly in control of the title race.
Hamilton will be at Mercedes’ Brackley headquarters between races, in the search for improvement and preparation work ahead of the sport’s first sprint race on the Saturday of the British GP weekend.
The Brit continued: “These past five races have been so difficult. Obviously I have lost a lot of ground in the championship so it has been pretty painful.”
The seven-time world champion stuttered to fourth at Sunday’s Austrian Grand Prix after he damaged his Mercedes by running over the kerbs at the final corner midway through the race.
Hamilton’s Mercedes boss Toto Wolff conceded that it is against the odds his star driver, who has signed a new £80million two-year deal, will win a record-breaking eighth title this season.
But the Austrian, who has overseen Hamilton’s remarkable run of success, believes the run of defeats for Mercedes will be beneficial for his team in the future.
“I am always the sceptical person, with the glass half empty,” he said. “But I am seeing the positives, and the positives are that there are 14 races to go, we are one DNF away from Red Bull, and we have lost more points than we should have through our own mistakes.
“We have not had the performance that we need to fight Red Bull. We are aware of that and we need to get our act together and hopefully perform better on the other tracks.
“After winning seven consecutive championships we are in a situation where we are fighting a tough battle. I wouldn’t say enjoyable is the right word but it is a new experience that will make us stronger in the long run.
“Every day is a new learning experience, and every day makes us stronger, even if we have so many consecutive weekends that are tough. We will look back many years from now and say that this was necessary.”