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|Lewis Hamilton celebrates victory in the 2019 British Grand Prix AFP/Andrej ISAKOVIC|
The measures will be introduced from June 8 to help curb the spread of coronavirus, but will reviewed every three weeks meaning an agreement could still be found in time for the Grands Prix to go ahead in July.
F1 stressed the need earlier this week for a quarantine exemption by highlighting the impact the new rules will have on "tens of thousands of jobs linked to F1 and supply chains."
However, Silverstone managing director Stuart Pringle is hopeful that an agreement can be reached that allows both races to go ahead.
"I am very clear that the importance of the industry is understood by government," he told Sky Sports.
"So I remain optimistic that a sensible and pragmatic solution, which puts the onus on the sport quite rightly to come up with the right solution, can be found."
Seven of the 10 teams on the Formula One grid have bases in England.
"This isn't just 90 minutes of an exciting sporting race. This is about getting an industry back to work," added Pringle.
"This is about 40-plus thousand people's livelihoods being ignited.
"The racing is at the very top of the pinnacle. Formula 1 is absolutely the top of the motorsport tree, it's the bit that we see and it's the most visible bit.
"But it is the stand-bearer for this industry and it's about getting an industry started again."
F1 organisers are hoping to start the season with the Austrian Grand Prix on July 5 behind closed doors, followed by a second race at the Red Bull Ring a week later.
It was hoped Silverstone could then host two races in back-to-back weekends, also behind closed doors.
The quarantine restrictions could also have a major impact on the participation of British sides in European football competition.
Manchester City, Manchester United, Chelsea, Wolves and Rangers are all still involved in the knockout stages of the Champions League or Europa League.
UEFA is planning for both competitions to be finished in August once domestic seasons have been completed.