Ferrari president Luca di Montezemolo, who has threatened to pull his team out of Formula One unless the 2010 rules are changed, will miss today's crisis talks with Max Mosley after the death of his father.
The champions were represented instead by team boss Stefano Domenicali.
Today's meeting with the International Automobile Federation (FIA) president, who has taken a low profile since the death of his son last week, will seek to end a standoff that threatens to tear the sport apart.
"I think this is a very important day, I think everybody feels we need to find a solution that makes sense for independent teams, manufacturers and the FIA," Williams chief executive Adam Parr told reporters as he arrived at the Heathrow airport hotel.
"Unfortunately we had an opportunity 12 months ago to do it in a more flexible and gentle way, and I fear time is running out."
The FIA want an optional £40m cost cap, offering greater technical freedom than available to those teams staying on unrestricted budgets, that they say is needed for the sport's survival in the face of the global financial crisis.
Ferrari, and former champions Renault, say that will lead to a two-tier championship that they cannot accept and have both threatened to leave.
Toyota and Red Bull's two teams have also said they cannot submit their entries by the May 29 deadline for the same reasons.
Formula One needs Ferrari but the Italian glamour team also need the sport, something that commercial supremo Bernie Ecclestone has been at pains to point out, and some sort of compromise may be inevitable.
"I must be clear that we, Ferrari and the others have no intention of breaking with FIA," Renault team boss Flavio Briatore said on Thursday. "We want to be there, to participate, to preserve the future."
With all eyes on the sport for the showcase Monaco Grand Prix next week, a key race for business and sponsorship deals, the teams will want to remove the doubts about the championship's future as soon as possible.
In contrast to the threats to quit, several would-be newcomers have expressed an interest in joining the championship if the cap stays in place.
Chassis maker Lola said they were forging ahead with their project in the expectation of the budget cap remaining.
"The Lola Group believes that the... decisions relating to cost-capping and the provision of revised technical regulations to facilitate the entry of new teams into Formula One should be embraced," it said.
"This is not only prudent considering the backdrop of global economics but also taking into account the need for new teams to be able to compete credibly against long established entrants.
"It is imperative that performance breaks be afforded to new cost-capped entrants who will have a limited period in which to form teams, design and manufacture their cars."