Personal injury, not personnel.
The gym owner has a duty to ensure all the equipment and the environment it is in is well maintained and in good working order. The owner also has a duty to ensure all the staff are properly qualified, trained and aware of their duties and responsibilities.
The manager has a duty to ensure that the staff are doing their job, that the environment and equipment are being used safely and properly.
They gym user has an obligation to use the equipment in a safe and proper manner and to take reasonable care of themselves. He will need to show that he didn't contribute to the accident by his own negligence - contributory negligence. Assuming he's not blind he can be reasonably expected to at least look at a piece of equipment before using it. This is assuming he has been properly inducted and instructed about using the equipment.
The lady who left the machine running is not liable as there needs to be a special relationship between the her and the injured person. This relationship arises where there is a contract between the two people or an obligation such as a doctor/patient relationship.
It goes further than that, though. You need to look at the tort doctrine of vicarious liability. This means that the employer is ultimately responsible if the employee fails in his duty of care in the work place. If there is a breached duty of care by the manager, the injured party would need to sue the gym owner - the council. Of course the employer could take action against his employee, but that is a matter for employment law.
In this scenario the manager would need to aware of the potential danger either by seeing it for himself or being informed about it by a third party. It is not reasonable to expect him or the staff to be closely monitoring every piece of equipment every minute the gym is in use. He can only be negligent if he failed to act as soon as he reasonably could be expected to.
In summary, you need to look at the tort of negligence, the duty of care and special relationship, breach of that duty, vicarious liability, contributory negligence.