As you may know, what determines speed of a chemical reaction is its kinetics.
I didn't read the BBC article, but charging a battery follows a simple reaction :
A + B(+) → A(+) + B
and the rate of this reaction is determined by:
R = K [A][B(+)]
as you can see it depends on K and concentrations.
the thing we can change to make the reaction speed really high is K.
K is determined by three things. first the nature of reaction and second the catalyst we use and we can change both and third the temperature.
so to make a super hell fast recharging battery you need to find the right material for reaction and right catalyst and right temperature.
I hope this was the answer you were looking for.