Covid: Hancock's vaccine buffer claims 'simply untrue' says first minister
But Mr Drakeford said Wales' success was based on the management of its own stocks, not any extra supply from the UK government.
People aged 25 to 29 in England can book to have their first dose of Covid vaccine, while in Wales more than half of 18 to 29-year-olds have had at least one dose of a vaccine.
He said UK ministers needed to make sure there was always enough supply for second doses, while Wales could draw on England's supply if needed
"We've drawn nothing out of an English buffer, we manage our own stocks and the fact that we have some of the best vaccination rates in the world is just because of the way in which the programme in Wales has been organised and delivered."
Mr Drakeford also said he was not prepared to follow England by announcing a date when all freedoms would be restored in Wales.
"I think it's too optimistic to say that vaccination has broken the link between falling ill and hospitalisation with the new Delta variant," he said.
"We really don't …
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