Some suppliers claim to be greener than others. This is blatantly not the case.
As far as I know, there is not an entirely separate network of green-coloured pylons crossing the country, which is only connected to green sources of energy such as wind, hydro, solar etc.
So any supplier which claims to be "green" is surely telling porkies, and the energy you receive will still contain energy generated from Coalborough-on-Trent coal-fired power station as much as any other supplier.
Green tariffs are certainly a bit of smoke & mirrors and clever accounting - at any given point you are receiving the grid mix, though this will vary by area (The Scottish Highlands with their abundance of renewables has a much greener mix than London which is much shorter on large scale renewables) - the tariff just ensures that for every kWh of energy you've used, at some point a kWh of green energy has been produced.
As far as I can see there are actually only two meaningful electricity suppliers, the National Grid and the local electricity company, and all else is just smoke and mirrors.
Neither National Grid or your local electricity company (aka DNO) are "suppliers" - but transmitters and distributors. They (usually) don't have any generation capacity and merely provide (& control) the infrastructure to get it from the points of generation to points of consumption. The 'suppliers' if you like are really those who own the actual generation sites, including EDF (UK's active nuclear fleet), Drax, RWE etc. Most of the Big 6 energy firms (and a number of the smaller ones too) have their own generation capacity as well as retail operations