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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The Department of Health is looking at new legislation to prevent pharmacists from being prosecuted for genuine dispensing errors.
The former England captain said he was "overwhelmed" by the messages he received from football fans after Rebecca died from cancer.
David Cameron said the measure, which will save £4 million by 2020, showed a commitment to his "all in this together" approach.