Hampshire Hospitals NHS Foundation Trust
The trust has private patients, but the website  indicates that there is currently no private patient unit:
Our private patient rooms are situated in the ward areas attached to the specific clinical environments. These rooms offer privacy and the comfort of en-suite facilities, television, radio and telephone and an a-la-carte menu. Your visitors will be made welcome during your stay and comprehensive catering facilities are available to them.
The trust provides amenity rooms:
Single rooms are sometimes available for patients who wish to have privacy and access to the facilities offered to private patients, without the expense of private healthcare. Your treatment will be delivered under the National Health Service, but you will be charged for the use of the room and additional services. If however during your stay, your room is required for a patient with clinical need, we will have to transfer you into a bay on an NHS ward.
The trust planned to have a private patient unit (at a cost of £2.5m) but this has now been deferred to delivery in 2013/14 because of the trust’s acquisition of Winchester and Eastleigh Healthcare NHS Trust. However, the trust says that the income from private patients will be limited :
Whilst the recent Health and Social Care Act allows for additional income to be earned from non-NHS sources, the vast majority of existing and forecast income is from contracts with NHS commissioners. Given the national pressure on NHS funding and the high proportion of income it represents, we recognise that the opportunities to increase income in the years ahead will be limited.
This would suggest that the trust regards private patient income as a limited income stream and that its main source of income is from the NHS, so it is surprising that the trust says that the reason for creating the unit is “income diversification”:
One response to this challenge has been a focus on income diversification … to reduce our financial dependence on local NHS commissioners.
And, further the Forward Plan  says:
Increased diversification of income away from local commissioners will be provided through our specialist services such as haemophilia, liver and Pseudomyxoma together with increased private patient income through a dedicated unit.