If lithium is being considered for extraction in the uk (such as Cornwall mining) then I think its fair to say the price for it must be high globally. This is to compensate for the additional costs in the uk (wages,regulation, transport etc) compared with the rest of the world.
When it comes to hydrogen, it's price will be based on supply, demand and extraction cost.
With electric vehicles there are many many forms of producing electricity. So now for each KWH you could have 4 or 5 different methods of production (nuclear,solar, wind etc) and maybe price war.
If I was an big petrol giant I would be trying to influence towards hydrogen.
Harder to store and to extract, much easier to maintain and control the price. More like the oil days rather than a future with too much competition.