Silverstone's deal ends after next month's race and talks are ongoing with the sport's commercial rights holders Liberty Media.
"F1 have admitted to us for the first time that they want to have a race in London," Silverstone Circuits managing director Stuart Pringle told the BBC.
"That's a material change because it's different to previous arrangements and Britain is not a very big island and it's a commercial concern.
"Throughout this process we have sought to manage the significant risk that comes with promoting an F1 race and this does nothing to reduce it," he added.
"In fact, it significantly increases the risk to Silverstone that only a few short years ago was nearly obliterated by its commitment to F1 and trying to maintain a British Grand Prix.
"We metaphorically and literally cannot afford to go back to that position."
Silverstone hosted the first world championship grand prix in 1950 and is a favourite venue for both the drivers and teams, most of whom are based in Britain. It drew the sport's biggest race day crowd of 140,500 last year.
Formula One has said it wants to keep the championship's historic venues but must also be run as a business.
There has long been talk of a race in London, most recently focused on the Docklands area to the east of the city. The all-electric Formula E series is due to stage a race there next year.
Ross Brawn, Formula One's managing director for motorsport, said in March that a number of areas on the peripheries of London could work.
"I think the question’s open. I don’t see that London would necessarily replace the British Grand Prix, it would be the London Grand Prix," he said then.
(Reporting by Alan Baldwin, editing by Nick Mulvenney)
