In the filing, the company has requested the use of an additional 24 antennas at Fawley, Wherstead and Woodwalton, bringing the total number of antennas at the site to 32.
It has also asked for a further 32 antennas at its Isle of Man site.
The application has been put out for consultation with the deadline for submissions on 31 May.
Ofcom said in the consultation form that it did not believe the expansion would interfere with rival services.
If approved, the request to vary four of neo-geostationary satellite system gateway licences would pave the way for SpaceX’s subsidiary Starlink to launch a mobile service.
The upgrades to its network would allow Starlink to do deals with British telecoms companies to boost their coverage, while it will also help with "supporting SpaceX's new direct-to-cell service (pending regulatory approval)".
Starlink is already testing a service in the US that would allow text messages to be sent from unmodified mobile phones via satellite, potentially resolving the problem of mobile black spots.
Currently, satellite-to-mobile services are not authorised in the UK, but it is understood that Ofcom plans to call for evidence on the technology in the coming months.
SpaceX’s network consists of almost 6,000 spacecraft, orbiting around 350 miles above the earth, which beam down broadband signals to satellite dishes for homes and businesses.
It is also launching thousands of new satellites that can connect to mobile networks. It already has deals in America with T-Mobile and partnerships with telecoms companies in Canada, Australia, Japan, New Zealand, Switzerland, Chile and Peru to expand its coverage.
Starlink has said that upgrades to its satellites will ultimately allow voice calls and internet data to reach phones.
Starlink has already signed a deal with Virgin Media 02 to provide mobile "backhaul", essentially providing extra capacity for the telecoms company’s mobile network.
But in the Ofcom submission, Starlink said further expansion would "grow the businesses of, and services provided by, local UK operators by enhancing Starlink’s cellular backhaul capabilities and supporting SpaceX’s new direct-to-cell service (pending regulatory approval)".
SpaceX added that its backhaul expansion and potential new mobile phone coverage could "allow customers to access an unprecedented level of connectivity. They will also facilitate partnerships with local operators, allowing existing operators to boost their connectivity options. More connectivity options will lead to more competitive prices for consumers."