Toto Wolff believed Mercedes had their 'best shot' to unseat Max Verstappen's run of five wins in a row at Silverstone, based on their historical performance at the track.
Lewis Hamilton has won a record eight times at Silverstone - seven of which came with Mercedes - while the team also won with Nico Rosberg in 2013.
Wolff expected their knowledge of the circuit to be a strength when speaking to media, including RacingNews365.com: "I thought that Silverstone - based on [our] historic performance - this was the best shot but it wasn't. So maybe there's another track where we have the best shot."
Mercedes introduced a major overhaul of their car in Monaco and it initially produced positive results for the team, with a double podium in Spain and a competitive run to third in Canada.
After Austria they were left conceding that Ferrari had made progress with their latest updates, while McLaren have started to catch up in the tight development battle behind Red Bull.
Wolff added: "The characteristics of the car have changed, but I always believe that we can we can beat Max. We're a good group of people, best drivers, we just have to give them a car that is more predictable and not Diva 2.0 and more complicated."
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Wolff: Important to find our way back to fighting for victories
The team did not expect McLaren to be as far ahead as they were during the British GP, with both Russell and Hamilton struggling to keep up with the straight line speed of the MCL60.
The Mercedes still appeared to suffer from high drag, which in turn affects their top speeds. Wolff said the team has been working hard to unlock "small gains" on the car, but concedes they may need to focus on a bigger picture.
"We've been fighting with the car for a year and a half trying to add performance. It came in, but it's just chipping away those small gains," he explained.
"I really see the positives because fundamentally, I don't care whether we finish second or third, it's important to find our way back to fighting for victories and the World Championship.
"While podiums are really happy for us, to see that the car has potential, fundamentally all sights are on the big prize and thats why it's exciting to see that McLaren was able to find a second of performance."