Most of our electricity used to come from burning fossil fuels, this is being replaced by wind, solar and other forms of green, renewable electricity.

Currently the UK National Grid gets between 40 and 60% of it's energy from Renewable Energy (excluding Nuclear which is arguably not renewable).
You can select your energy supplier to obtain all their energy from renewables.

When the National Grid has sufficient energy storage worries about where the energy will come from on windless, cloudy days will be null and void. Such storage options are being rapidly rolled out and innovative solutions being developed such as  Liquid Air, using Nitrogen to compress air to a liquid using off peak or excess wind or solar power then releasing it through a turbine to generate electricity (see High View Power), Iron Air batteries: a new technology being developed that looks very promising and various uses for coal mines such as Graviticity and even converting them into geothermal energy souces.

There are other sources of green energy, whilst the UK's capacity for Hydro-electric power is limited, great strides are being made in tidal turbines which could suppy reliable base load energy (i.e. energy that is not wind or sun dependent and can replace gas, oil and coal fired power stations.

Note that Carbon Capture and Storage is still in the theoretical stage with the very best experiments anywhere in the world capturing only 6% of emissions, treat suggestions that it can capture the majority of carbon emissions with a healthy amount of scepticism.