Prodrive have abandoned their bid to enter Formula One in 2008 because of Williams' threat to take legal action over their plan to use customer cars.
Richards hopes his team will be able to compete in F1 in the future
Prodrive wanted to race in cars bought from McLaren-Mercedes, but have been forced to delay joining the grid.
"It is disappointing to face a last-minute legal challenge when our plans have been public knowledge for over a year," Prodrive said.
However, the team still hopes to enter the championship at some future date.
A customer car is a vehicle manufactured by a constructor and sold to another team to race.
The guiding force behind Prodrive, who run the Subaru world rally championship team and would have been the 12th team in F1, is former BAR and Benetton chief Dave Richards.
Under the Concorde Agreement, the secret document which governs F1, customer cars have always been illegal.
Prodrive had pledged to enter F1 after motorsport boss Max Mosley said that rule would be changed from 2008 but Williams launched a legal challenge to this and Prodrive's bid to race customer cars.
Recently, a new Concorde Agreement has been negotiated, but not yet signed, and it is unclear how that affects the issue of customer cars.
The climate of uncertainty has led to the decision to skip the 2008 championship.
"It is still our ambition to compete in Formula One," Prodrive said in a statement.
"We are hopeful that a new Concorde Agreement between the FIA, FOA (Formula One Administration) and teams will provide clarity as to the terms on which this might be possible.
"When this new agreement is reached, we will be in a position to consider the extent to which we can adapt our plans for participation in the future."