Campaigners say vehicles that use “sustainable fuels” should be exempt as they help to “reduce pollution”. This is because the sustainable fuels will use “existing pumps and infrastructure”.
The petition is expected to run for six months and has a deadline of 21 December.
So far just 413 signatures have been received with 10,000 needed for a Government response.
The rule change could be debated in the House of Commons if 100,000 signatures are received.
Sustainable fuels are made from renewable materials instead of traditional petrol or diesel fuel.
Historic Classic and Vehicle Association spokesperson Malcolm McKay also said e-fuels would be ideal for classic car owners concerned by electrification.
He said: “E-fuels, with green generation, are potentially carbon-neutral and are the most viable answer for aircraft, ships and long-haul trucks.
“They offer an achievable solution for poorer countries with older vehicle fleets and inadequate electricity infrastructure.
“They also offer a lifeline for historic vehicles.”