Hancock told BBC Breakfast this year's programme was "more important than ever" because it is "very dangerous" to get both flu and Covid at the same time.
Those over 65 are already eligible for a free flu jab and the health secretary said this group was "the top priority".
In response to concerns GPs would not have enough staff or resources to deliver the programme, he admitted it would be a "huge amount of work for the NHS" and said he was "very grateful" for the efforts of staff.
Wales FM: Talks over UK-wide Christmas rules ongoing
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Talks between the four UK nations over restrictions for the Christmas period are under way, Wales' First Minister Mark Drakeford says.
Drakeford said he hoped for a "common approach" to travel within the UK after differing restrictions in recent months - Wales ended a "firebreak" lockdown this week as restrictions continued in England and Scotland.
He told BBC Radio 4's Today programme: "We agreed some broad parameters on Wednesday and remitted officials of all four administrations to work now on the detail, so I remain hopeful that it will be possible to reach a four-nation approach to Christmas.
"I certainly think that is the right thing to do - if it is achievable - and certainly Wales will be at the table next week looking to find an agreement."
Drakeford said an agreement on permitting travel across the UK during the Christmas season was "top of the list of things to agree", even if a wider agreement was not possible.
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