Proton beam therapy units (whether the low energy unit at Clatterbridge, or the two new proposed high energy units) require significant public investment.
The relative small numbers of private patients that can use these units will have little effect on the revenue generated by facility and the vast majority of the income for these units will be from NHS commissioners. Therefore, it is unjustified to say that these facilities cannot exist without the income from private patients. It is clearly the case that private patients will benefit from public facilities, rather than public facilities benefit from the income of private patients. Since these facilities are scarce resources, unless there are explicit reassurances otherwise, it is reasonable to say that private patients are paying to jump the queue.