First, why "It does not matter if your supplier does actually the missing two thirds of your power at a later date from a renewable supplier"? (btw, we talk in energy not power) Energy use is replenished by renewable sources. The most important thing is that funding does not go to fossil fuel energy sources. Assuming supplier sticks to their contract, which brings us to second point.
Second, what makes you so sure all energy supplier will break contract? You've seen the certified sources claims, if you question this, you should be able to request their certificates and dig deeper to find out for yourself. I trust there are regulatory bodies to ensure no false advertising.
Third, the UK grid is getting cleaner year by year. IF for some reason an EV driver isn't on green supplier, all EV will still get greener as it ages because the grid is getting greener.
https://www.nationalgrid.com/uk-hits-major-clean-energy-milestone
True, EV charged during peak times are more likely to be natural gas powered than renewable. It is clear from grid carbon intensity data. But it doesn't mean the owner is paying the gas company for the privilege. This is important because green suppliers give people ability to vote with their wallet. Which in turn allows building more renewable sources, which allows the nation to be less reliant on fossil fuel.
So I have grasped what you are getting at, but you are, once again, ignoring the big picture. Only looking at instantaneous energy generation while ignoring the benefits of green suppliers and overall economics of energy suppliers.