Lodged on the official Number 10 website, the petition calls on Brown to bring the BBC in line with current European Broadcasting Union standards by restoring the correct transmission bandwidth on the channel. It has already attracted 206 signatures.
After the BBC introduced new encoders on August 5, the bitrate on BBC HD dropped from 16Mbs to 9.7Mbs, a reduction of nearly 40%. Satellite viewers subsequently reported various problems with picture quality and sound on the channel, with some accusing the BBC of failing to deliver a truly HD service.
In a statement, petition creator Lawrence Wilkes said that despite the numerous complaints, the BBC has remained steadfast in its belief that there is not actually a problem on the channel.
"It is widely believed that the reason for the reduction in bandwidth is so that the forthcoming Freeview HD channel, which cannot achieve the same bandwidth as satellite, does not suffer in comparison," he continued.
"However, the problem this creates is that the BBC HD is still compared to other broadcasters on satellite, and the BBC's own HD transmissions before August 2009, all of which are visibly superior to the current BBC HD channel in terms of picture quality.
"The BBC could overcome this and satisfy viewers by simply restoring the bandwidth allocated to BBC HD to the previous levels. However, the BBC appears reluctant to do this, but more frustratingly are unwilling to state why."
Earlier in the month, BBC principal technologist Andy Quested discussed EBU recommendations as part of his technical briefing series in response to the picture quality controversy.
Before Christmas, consumer publication Which? ran independent tests of BBC HD material from the new and old encoder, but found that any difference in picture quality was "insignificant".