I think the Conservative Party thinks Hunt is doing an excellent job. He remained as NHS minister after the election. Why would he stay in post if there was any sense that he was making a mess of it.
Looks to me as if he is pushing forward their agenda to privatise the health service, and (in their eyes) making a success of a very difficult task.
Either they think he has not yet finished the job (in which case he'll remain as Health minister and given a promotion later), or they think he has pushed it far enough that someone else can take over and he'll be given a big promotion.