Boris Johnson has argued that teachers, carers, police officers and other key workers should be vaccinated "as soon as possible".
Speaking at Prime Minister's Questions, Conservative MP Jason McCartney (Colne Valley) asked: "Does the Prime Minister agree that once we've vaccinated the most vulnerable, the elderly and our wonderful health and social care workers, we should then look at prioritising vaccinating police officers, emergency service workers, carers, teachers, nursery staff and all those whose essential daily work brings them into contact with other people?"
Mr Johnson replied: "We must rely on what the JCVI (Joint Committee on Vaccination and Immunisation) has to say.
"There are priorities that the experts have decided, but of course we want to see those groups that he mentions vaccinated as soon as possible.
"I am very pleased that in spite of all the difficulties, we gave 1.5 million people their first dose - up half-a-million on the week before."
A total of 4,419,704 Covid-19 vaccinations had taken place in England between December 8 and January 19, according to provisional NHS England data, including first and second doses, which is a rise of 301,362 on Tuesday's figures.
Of this number, 3,985,579 were the first dose of the vaccine, a rise of 298,3730 on Tuesday's figures, while 434,125 were the second dose, an increase of 2,989.
The vaccine is currently being given to four groups, NHS staff, the clinically extremely vulnerable and everyone over 70.
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The government is aiming to get these four groups vaccinated by February 15, and will then move down the priority list.
Currently the JCVI say the next group to be vaccinated should be the over 65s but there are growing calls for key workers such as teachers to get the jab next.
