Alonso produced a lap of one minute 25.252 seconds right at the end of the session on a drying track but the time - more than five seconds slower than the fastest in pre-season testing at the Circuit de Catalunya - was purely a crowd-pleaser.
Plans to provide more track action by giving drivers an extra set of prototype long-lasting hard tyres were stymied by the weather, with leaden skies and drizzle replacing Friday's sunshine.
Felipe Massa was just behind his team mate in 1:25.455 while Frenchman Jean-Eric Vergne was third fastest in a Toro Rosso with compatriot Romain Grosjean fourth in a Lotus.
Red Bull's triple world champion and overall leader Sebastian Vettel was 19th quickest of the 22 cars, waiting until the track was drying late in the session before venturing out for a proper lap, with Australian team mate Webber 20th.
Kimi Raikkonen, second overall and 10 points behind Vettel, managed the eighth best lap for Lotus.
All teams have brought updates to the first race of the European season but former champions McLaren and Williams have more riding on them than most after struggling in the first four races in Asia and the Middle East.
The weather deprived both of the chance to put in meaningful miles, with Button and Mexican team mate Sergio Perez spending part of the session watching from the garage as McLaren erred on the side of caution.
Button was already resigned to that before the session started, however.
"We won't be running so much in the wet. When you turn up to a place with new parts, you don't normally have a lot of them so I don't think we'll be doing a lot of wet running," he said.
McLaren sporting director Sam Michael added: "We've got enough parts for two cars, but we're limited on spares so we'd like to avoid crashing or going into gravel."
Button, the 2009 world champion, has finished no higher than fifth so far this season after winning the final race of last year in Brazil with what was then deemed to be the fastest car.
McLaren, who brought out a significantly new car this season instead of the more evolutionary approach favoured by others, have been working overtime to fix the aerodynamic problems with the team using up one of their 'jokers' so mechanics could break an overnight curfew.
"I think we have to reserve judgement until we actually drive the car. There's a lot that's different," Button said.
"It looks nice. There's some really cool looking little bits on the car but I don't think it's going to be enough to really fight right at the front," he added. "I think we will see an improvement and hopefully that will help us understand the air flow of the car a little bit better."
"If we get a good correlation between this circuit and the wind tunnel, that's just as important as seeing an improved lap time this weekend."