The Downing Street petition has 3,907 signatories who want to see spectrum set aside for high definition services rather than it being sold off to mobile companies.
'Countries such as America and Australia are already rolling out this technology but Britain has been left behind because of the lack of spectrum space,' the petition states.
The BBC, ITV, Channel 4, Five, Samsung, DSGI, Toshiba and Sony recently joined forces to launch an HD for All campaign.
Speaking at Broadcast's HD Here and Now conference today (Tuesday 20 February), the BBC's head of HD Seetha Kumar said:
'Ofcom is currently consulting on the use of this spectrum, and has proposed a technology-neutral auction which it believes will achieve the most efficient spectrum use.
'But distributing on DTT in HD imposes substantial additional costs on all broadcasters, with no obvious return for free to air commercial broadcasters, while the BBC has to operate within a fixed licence fee.
'There is a case for Ofcom to consider reserving some of the digital dividend spectrum for HD channels in order to safeguard the future health of Freeview, which has proved itself so popular with viewers, and to make the high quality of HD available to all viewers whatever their choice of platform.
While it is unclear whether the BBC's high definition proposals will be given the go-ahead under the less than expected licence fee, BBC insiders say that director general Mark Thompson is a strong advocate of the technology.
The BBC will shortly submit its proposals to the Trust who will in turn decide whether it should be put to a public value test - the same regulatory process currently under way for the BBC iPlayer.
Kumar said that any BBC HD service would inevitably launch with limited content, and would be based, as the trial has been, solely on HD originations.
'Its growth would be evolutionary as more native HD content comes on stream,' she said.
'I can also say that BBC HD broadcasting will not be equivalent on all platforms at launch, because of the insurmountable restrictions on terrestrial capacity while we have dual analogue and digital transmission - but that our aspiration over time would be to be universally available on all technically capable platforms, as far as possible.'
The BBC's HD trial is due to run until June.