I very much doubt it. The essence of such a project would be to identify wasteful activities and reallocate or remove the resource. In simple terms that means getting rid of wasteful activities (duplication of actions, unnecessary data entry, better flows which reduce meters travelled by patients and employees, that sort of thing) and either getting the person who was doing that to do something else which is necessary and adds value or, if there’s nothing else they can do or are needed to do, getting rid of that person.
I can’t ever see a Union allowing that to happen; their members changing activity and many of them losing their jobs. Unions are not there to act in the national interest or in the interest of anyone who is not their member. The Consultants Unions, the Nurses Unions, the Porters Unions, the Admin Unions etc; they will all act to stymie any improvements and the rest of us be damned.
Of course for the conversation to even start there would have to be an effective senior management in place and I see no evidence of that either.