Qualifying 18th, with Spanish team mate and double world champion Fernando Alonso 17th, the Briton was quicker only than the two tail-end Manor Marussia drivers who have what is essentially a modified 2014 car.
McLaren, the second most successful team in the history of the sport, are enduring a nightmare with no immediate end in sight.
They have had their worst ever start to a season and scored just four points in eight races with a car that is way off the pace in the first year of their new partnership with Honda.
At the previous race in Austria, both drivers collected 25 place grid penalties -- with only 20 cars competing -- as a result of engine and gearbox problems. Neither finished on Sunday.
Saturday's Silverstone agony was compounded when the team put one of Button's tyres on Alonso's car -- prompting another joke by the Briton that it explained why his team mate had been "so quick".
"It wasn't the highlight of the year," said Button, diplomatically, of once again going out in the first phase of qualifying.
"In front of the home crowd you always want to have a great weekend and I think the fans understand the position we've been in for the whole season.
"It was always going to be difficult this weekend...but I hoped for more," added the 2009 world champion, who has never stood on the Silverstone podium in 15 years of trying.
McLaren Racing director Eric Boullier said McLaren were putting pressure on Honda to improve the engine as fast as possible because the lack of success was hurting.
"I keep telling (Honda motorsport head Yasuhisa) Arai every day that we need to be successful as soon as possible. (I tell him) twice a day and three times a night because of jet lag," said the Frenchman.
"The pain is real, there is nothing we can hide.
"We put pressure on Honda, they put pressure on us. Maybe more is on them so far because we need to have more performance from the package of the car and engine. More than 50 percent and much more of that will come from the power unit."
(Editing by Mark Meadows)
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