Following his third place in Sunday's Canadian Grand Prix, Hamilton said: "I don't leave here thinking I'm going to Silverstone with the possibility of winning. Not when I've just seen the pace of the Ferrari and the Red Bull. They are massively quick.
"Sebastian Vettel [the world champion and current leader] was pulling away from me at a second per lap. We're not going to gain a second before the next race. But we can definitely beat the rest.
"I think Silverstone will be a real challenge for us. Tyre degradation will be a real challenge for us there. There are lots of high-speed corners so there is lots of opportunity to degrade the tyres. Winning the GP there in 2008 was unlike any other experience I have had."
After Sunday's race Button said McLaren would have some upgrades coming in time for the Silverstone race on 30 June, but that they would not be enough to put his car at the front. At this rate British fans' best chance of a home success rests with Force India's Paul di Resta.
Hamilton's performances with Mercedes have been much stronger than expected, and he lies fourth in the drivers' standings. But he was surprisingly downbeat in Canada. "What I'm projecting is not disappointment. I've just got stuff on my mind," he said.
Hamilton said he has been urging his Mercedes team to close the gap with the championship leaders, Red Bull and Ferrari.
He said: "I've just said to the guys we need to work harder. We have a great qualifying car, and it feels great in the race now. But we need to make another big step. There are things on other cars which we haven't got. Things on the Ferrari and Red Bull, and I'll say: 'Why haven't we got that?' And they'll say: 'We're testing that in three weeks.' And I'll say: 'Why not test it now?' I always try to keep pushing the guys."
Hamilton said he is not spending time worrying about McLaren, who are sixth in the constructors' championship and falling further behind Force India. "That is not something I am focusing on," he said. "McLaren are a fantastic team and I am sure they will bounce back. They have a great leader and I'm sure they are working as hard as they can. They have had some results where they have beaten me. This is just one race."
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