Mr Hancock told Sophy Ridge on Sunday: "We've asked the expert group, the Joint Committee on Vaccination and Immunisation, what order we should vaccinate in, broadly in order to reduce the number of deaths as fast as possible.
"I think everybody can understand why we asked that as the question.
"They set out the priority groups one to nine, which includes those who are clinically most vulnerable and their carers, and includes the over-50s, going down the age range.
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"They are currently considering, after that, what might be the best order in terms of clinical priority.
"There isn't strong evidence that teachers are more likely to catch Covid than any other group, but I'll leave it for the JCVI to set out what they think is the best order in which to do this that minimises the number of deaths."
Mr Hancock said the Government believed it had the vaccine supplies to meet the new target of offering all adults a jab by the end of July.
“We now think that we have the supplies to be able to do that, we can see the NHS and all of those partners and all of those working on this have been able to deliver jabs at about half-a-million a day, which is an incredible effort.
“So, collectively, the whole team now needs to focus on this renewed target of all vulnerable groups, all those over 50 by April 15 and then we will keep rolling out and make sure that all adults get access to the jab.”
Matt Hancock has also insisted it is right to take a “cautious” approach to easing lockdown restrictions despite the vaccine programme going “very well”.
The Health Secretary said: “It is right to be cautious – it is incredibly important. There are still almost 20,000 people in hospital with Covid right now…
“The vaccination programme, whilst clearly going very well, will take time to be able to reach all people who have significant vulnerability, especially because we need to get the second jab to everybody.