Martin Leiws (the man who is so often on the TV helping us to save money) has a free service which makes switching to a green energy provider easier. His long-standing 'Cheap Energy Club' website now has a way of prioritising green energy tariffs when generating market comparisons.
You can toggle the importance of factors, to ensure tariffs are suggested which suit your preferences (e.g. green energy, customer service...)
I tried setting only the 'Green' toggle to see which tariffs were suggested. I made a note of them. Then I used the handy (and reassuring) option of 'Use Martin's preferences' which toggles a good spread of price, green and customer service (it turns out that Martin Lewis doesn't put too much weight on a 'well known supplier' he favours a good customer-service record instead).
I found that one of the 'green' tariffs which appeared during my first comparison, also came up when I was using 'Martin's preferences'. This really did make choosing a new (green) tariff much easier and less scary.
So why not try switching to a green energy provider (let Martin Lewis do all the hard work for you), once your current tariff is up?
*EDIT* It turns out that there are degrees of green - some green energy companies are much greener than others...
Energy companies are able to label their tariffs as 'green' even if they just offset fossil fuel produced energy with something called a REGO certificate. After hearing about this 'greenwashing', if I can afford it, I'd rather choose an energy company which invests in / encourages renewable infrastructure, such as Ecotricity, Good Energy and Octopus Energy (which also supplies Co-op Energy)
A Which? report from 2019 gives a good overview of green-ness, although finding more up-to-date information is tricky... good luck!