I do not really see if many extra measures need to be put into place. This is leaning towards a nanny state where people will not take responsibility for their own actions.
Of course they have a duty of care, most certainly for staff and guests. Talking specifically for the guests, not much more than the usual. People are choosing to visit the park on those days, so they should be responsible for their own actions. With staff it is slightly different, but I am talking specifically about guests. Alton Towers are pretty flexible when changing dates due to extreme circumstances so I do not see this being any different. If people still choose to go, then they need to be responsible for their actions and stop expecting to have to be nannied throughout their day when they have made the conscious decision to go on that day.
That said, it would not hurt for extra water stations, sun cream and what not, possibly some extra shade in ride queues, which I think they most likely will do. But beyond that, I do not think it is Alton Towers responsibility to be honest.
With staff however, it is a very different kettle of fish.