The vaccines minister has said he is hoping to target key workers such as police officers, shop workers and teachers in the next phase of the vaccine rollout.
Officials have so far been prioritising the over-80s, NHS staff, and care home residents and staff as they are classed as the most vulnerable.
Vaccines minister Nadhim Zahawi told Sky News that while groups will continue to be prioritised "based predominantly on age and vulnerability" to COVID-19, the second phase of the rollout could see the vaccine given to those who are most likely to come into contact with the virus at work.
"My very strong instinct is that those who through their work may come into contact disproportionately with the virus, police, shop workers, teachers... should be prioritised," he said.
Mr Zahawi will be working with the Joint Committee on Vaccination and Immunisation (JCVI) to establish who will get the next shots in phase two of the rollout, with a decision expected to be made by mid-February.
Currently, the order of priority for groups in phase one is:
1. Care home residents and their carers
2. Those 80 and over, and frontline health and social care workers
3. Those 75 and over
4. Those 70 and over, and clinically extremely vulnerable people
5. Those 65 and over
6. People between 16-65 with underlying health conditions which put them at risk of more serious illness from COVID-19
7. Those 60 and over
8. Those 55 and over
9. Those 50 and over
But unions have been calling for more key workers to be vaccinated as they are among the most at risk of catching the virus.
A petition calling for teachers, school and childcare staff to be prioritised has gained more than 470,000 signatures, with some arguing it could pave the way for schools to reopen.
Meanwhile, chairman of the Police Federation John Apter has called for police officers to be given the vaccine as soon as possible.
The call has been backed by Dorset Police after two officers tested positive for COVID-19 days after policing an anti-lockdown rally in Bournemouth.
One of the officers, who did not want to be named, said the virus had "never made him feel so ill" and he is unable to get out of bed.
"Police officers shouldn't be the first in line for the vaccine and we know the risks of our job, but we see vast amounts of people every day," he said.
"If a call comes in, we have to go to it; we can't say we won't go to it. And we are putting ourselves, and our families at risk, every single day."
The JCVI has stated that the "key focus" for the second phase of vaccination "could be on further preventing hospitalisation".
But it acknowledged that those at increased risk of catching the virus due to their occupation "could also be a priority".
"This could include first responders, the military, those involved in the justice system, teachers, transport workers, and public servants essential to the pandemic response," it said.
Last week, a member of the committee, Professor Adam Finn, told Sky News' Sophy Ridge On Sunday programme that no decision had been taken yet but the "critical role" of teachers would "figure in the discussions".
Health Secretary Matt Hancock has also previously signalled that there is a "good case" for relaxing the allocation by age groups once the most vulnerable people and over-70s have been given the jab.
"Once we've got through the clinically vulnerable groups, then we've got a debate to have as a nation about where we go next," he told ITV.
"And I think that teachers and police officers, actually in shop workers have got a good case that they should be next, as opposed to just carrying on through the age range. We haven't made a final decision."