Dr Sarah Jarvis has told Daybreak that it would be "difficult" to impose a seven-day rule on GPs and hospitals.
She said: "This is not going to be free, there's going to be a lot of bureaucracy and that means more cost for the NHS and patient care would suffer."
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Cooler and fresher across the UK over the next few days.
The prime minister was shouted at as she left the scene of the tragedy in which at least 79 people died.
Father-of-six Makram Ali, 51, was already receiving medical treatment as the attack unfolded. He died from multiple injuries, police say.