The once dominant team, winners of nine constructors' championships between 1980 and 1997, have not scored in the last eight races and are locked into their worst ever start to a season.
Venezuelan Pastor Maldonado's against-the-odds victory in Spain last season was their first in nearly eight years and the team has only gone backwards since. It has been a decade since Williams came close to winning a constructors' championship.
The only bright spot in an otherwise depressing campaign has been Finnish rookie Valtteri Bottas lining up third on the grid in a rain-hit Canadian Grand Prix qualifying - before the hopes vanished in the race.
Even if a win for Williams on Sunday would be a bigger shock of the British sporting summer than Rafael Nadal's first-round exit at Wimbledon, Silverstone is full of positive energy for a team proud of its past but very much focused on the future.
"I wake up every morning determined to get us back to the top," said team founder and principal Frank Williams in comments to mark the anniversary.
"Williams should be fighting for championships and I am confident that we will be doing so once again."
It will be a long and hard road back but there is still huge goodwill in the sport towards a fiercely independent and proudly British team who rank as the second most successful after Ferrari in terms of constructors' titles.
They have 114 wins, 127 poles and seven drivers' championships to their credit with the likes of Alan Jones, Keke Rosberg, Alain Prost, Nigel Mansell, Nelson Piquet, Damon Hill and Jacques Villeneuve.
They have also lived through dark days, the 1986 road accident that left Williams paralysed and wheelchair-bound and the tragedy of Brazilian triple champion Ayrton Senna's death in one of their cars at Imola in 1994.
"Frank and (co-founder) Patrick (Head) are both legends. I raced for them in 2000, they gave me the opportunity to race in Formula One," said 2009 world champion Jenson Button, who began his career at Williams when they were in partnership with BMW.
"I've got great memories with them and with the whole team...it's a true racing team and that's what I love about it.
"With belief and determination he's achieved, or the team has achieved, so much in their career," added the Briton. "Six hundred grands prix. It really is phenomenal. Fair play and hopefully they will be here for many many more years."
In fact, the 600th race will be in Germany next week - with the team counting from the foundation of Williams Grand Prix Engineering in 1977 with a staff of 17 working out of an old carpet warehouse in Didcot - but Silverstone is home.
"Our foundation and our longevity is a testament to the thousands of people who have sacrificed so much to keep us here," said Frank Williams. "It seems only right to mark this milestone at the home of British motorsport alongside our loyal British fans."
Flush with Saudi cash, the team took their first race win at Silverstone in 1979 with Swiss driver Clay Regazzoni and celebrated their 100th win at the former airfield in 1997 with Canadian Villeneuve.
Since their foundation, 78 Formula One teams have come or gone or changed ownership but Williams are still battling on - even if the cars currently coming out of the factory are far less successful than the ones in the museum inside and sponsorship is harder to find.
In Germany, the FW35 cars will have the number 600 on the sidepods while the livery will also carry the names of the group's 691 employees.
"This weekend we will be rightly celebrating our heritage and reflecting on some of our defining moments over the past 36 years," said Claire Williams, Frank's daughter and now the deputy principal.
"This is also an opportunity for us to take stock and look ahead to the future, making sure that we have the necessary pieces in place to make our next 600 races just as memorable."