Current economic instruments aimed at climate change mitigation focus mainly on CO2 emissions, but efficient climate mitigation needs to focus on other greenhouse gases as well as CO2. This study investigates the distributional effects of climate change taxes on households belonging to different income and lifestyle groups; and it compares the effects of a CO2 tax with a multiple GHG tax in the UK in terms of cost efficiency and distributional effects. Results show that a multi GHG tax is more efficient than a CO2 tax due to lower marginal abatement costs, and that both taxes are regressive, with lower income households paying a relatively larger share of their income for the taxes than higher income households. A shift from a CO2 tax to a GHG tax will reduce and shift the tax burden between consumption categories such as from energy-intensive products to food products. Consumers have different abilities to respond to the tax and change their behavior due to their own socio-economic attributes as well as the physical environment such as the age of the housing stock, location, and the availability of infrastructure. The housing-related carbon emissions are the largest component of the CO2 tax payments for low income groups and arguments could be made for compensation of income losses and reduction of fuel poverty through further government intervention.