Brian
You appear to have little or no knowledge on public procurement which is controlled by law imposed on us by both WTO and the EU. We cannot do what you want even if we wished to.
There is no" transferring of money to private pockets" which is what you keep claiming.
In a very brief nutshell, if there is a service such as cleaning, the authorities will identify a cost against a given service level.
The work can be put out to tender and even if a private company comes in with a lower price, the NHS is nearly always given the opportunity to match the price.
If they cannot or will not match the price, then the company offering the best value for money will usually get a 3 year contract. The NHS staff are protected by TUPE and job losses are almost non existent. At the end of the three years, a new tender exercise is conducted and once again the NHS authority can apply to be included. If no supplier comes forward to tender, the work comes back to the NHS.
There is no transfer of funds, the NHS is still owned by the taxpayer and the service, which is always monitored by the NHS, is temporarily transferred for the three year period and the savings have to be identified by law and these are nearly always passed onto other budgets which allows more goods such as medicines to be bought.
Mick