A similar argument shows that Tom’s unexploitable bluffing frequency is $b= frac{1}{3}.$ John can maximally exploit any deviation from this strategy by either always calling with K♠ ($c=1$), if Tom bluffs too often, or always folding with K♠ ($c=0$), if Tom doesn’t bluff often enough.
If either player uses his unexploitable strategy we have
[ E(T) = frac{1}{18} ]
so Tom wins on average £1/18 = 5.5p per hand.