The provider you go with is a really important question, but actually quite a complicated one because there's a lot of confusion about suppliers / tariffs that are genuinely green, and those that are simply marketed as green (otherwise known as 'greenwashing'). Below is some context on this distinction and then a couple of recommendations for suppliers to look at. Ultimately, you'll need to look at the specific tariff you're offered and how it's composed to know if you're getting a green electricity supply.
Firstly, it's not strictly possible to get your electricity supply from the National Grid and for that supply to be 100% renewable. The only way to ensure that only 100% renewable electricity is supplied to your business is to connect directly from a generator (e.g. install your own solar panels). This is because the various different energy sources (coal, gas, wind, solar etc.) are sent to the National Grid where the energy is 'mixed up' and distributed to households and businesses. It's this that leads to discussions/media coverage of the UK's energy mix. Currently about 30-40% of the UK's energy supply comes from renewable sources. In an ideal world that supply would be 100% renewable (or certainly much higher than currently).
For a tariff to be genuinely green, it needs to be from a supplier that sources their electricity directly from renewable generators (e.g. a wind farm). Even better if your supplier directly invests in new renewable electricity generation themselves. You should not buy from a supplier that just buys cheap REGO certificates (explained below), as this does nothing to increase demand for or supply of renewable energy.
The problem comes from the fact that it's very easy (and perfectly legal) for an electricity supplier to present their tariff as 'green' when it's doing nothing to stimulate demand for renewable electricity. This is based on the existence of Renewable Energy Guarantee of Origin certificates (known as REGOs), which verify renewable energy generation and can be traded between suppliers. It gets quite complicated, and we can provide more information, but essentially means that a supplier can buy these certificates very cheaply to present their tariff as 'green' when the underlying energy may be from fossil fuel/brown sources.
This also has an impact on cost, with genuinely green tariffs often costing more due to the additional costs of sourcing renewable electricity directly, so if you see a green tariff that is very cheap the odds are that it's not actually green at all. All of this means that you should look for a tariff that is backed by 100% renewable electricity rather than 'greenwashed' with the purchase of REGO certificates.
Recommendation: Now in terms of specific suppliers, we often suggest looking at Ecotricity and Good Energy, which regularly come out on top in terms of sustainability when ranked by independent sources such as 'Which?'. The bottom line though is that you'll need to look at the specific tariff as many suppliers will also have mixed/non-green tariffs.