As the petition explains:
"The tax payer and/or energy consumer is currently paying to subsidise low carbon technology through a variety of levies and subsidies that share no common price for their efficacy in reducing carbon (or C equivalent) emissions. A well designed tax on carbon emissions, in concert with internationally agreed application methodology, would deliver huge cost and carbon savings to society, with parity and without excessive and costly bureaucracy. We the undersigned urge Government to press to replace costly local, regional and national policies with a global approach that reflects the unity achieved in the removal of CFC emitting products."
There are many details not covered in this petition, but that is the nature of an online petition. I understand that Nick wanted to add a detail that I suggested (to address many people's fears with regard to the impact on "fuel poverty"), but the system wouldn't let him.
Fundamentally, carbon tax is the best way to internalize carbon externalities, and showing support for the principle is important. If you would like to see our myriad nit-picking, micro-managing, counter-productive, bureaucratic, supposedly-green interventions replaced with one simple mechanism that applies equally to all carbon emissions regardless of source, then sign up to this petition now.