GP practices will receive a letter this week setting out details of the role they will be expected to play in delivering a vaccine, and advising them that they should be ready to start before Christmas if a product is approved.
However, comments from DHSC officials suggest the possibility of a vaccine becoming available this year remains slim.
BMA leaders confirmed talks with the government over plans to deliver a vaccine - but GPs have hit out at the announcement of a deal before it had been 'negotiated or voted on'.
A DHSC spokesperson said: 'While there are no certainties in the development, production, and timing of new vaccines, there is a possibility a COVID 19 vaccine could be available in the UK in the first part of 2021.
'It will only be rolled out once proven to be safe and effective through robust clinical trials and approved by medicines regulator the MHRA.
'Once approved, the NHS stands ready to begin the vaccination programme to those most at risk, before being rolled out more widely.'
Sir Simon told the BBC's Today programme on 4 November that over 200 vaccines were in development and 'we believe we should get one or more available certainly from the first part of next year'.
He added: 'We are also gearing the NHS up to be ready to make a start on administering COVID vaccines before Christmas if they become available.
'We have reached agreement with the GPs to ensure they will be doing that, we will be writing to GP practices this week to get them geared up to start before Christmas if the vaccine becomes available.'
According to a priority list published earlier this year by the Joint Committee on Vaccination and Immunisation (JCVI), which advises the government, care home residents and staff could be first in line for jabs, with health and social care workers and people aged over 80 next.
The NHS chief praised GPs for 'doing a brilliant job' alongside pharmacists in delivering flu vaccines - with 2.5m more flu vaccinations completed now compared with the same stage last year.
BMA GP Committee chair Dr Richard Vautrey said: 'The BMA fully expects general practice to play a significant part in the roll-out of any COVID-19 vaccination programme. Our GP committee is therefore naturally in discussions with NHS England to help plan and prepare for this, however, as yet we do not have a specific date when the vaccines will be ready.'
However, GP committee member Dr Kieran Sharrock wrote on Twitter that the 'agreement' announced by NHS England had 'not been discussed' with GPC England to his knowledge.
Bristol GP Dr Shaba Nabi also hit out at the announcement - calling for NHS England to explain 'why there are announcements about GPs delivering a COVID vaccination programme before Xmas when the deal hasn't even been negotiated or voted on'.
Could someone @NHSEngland explain why there are announcements about GPs delivering a Covid vaccination programme before Xmas when the deal hasn't even been negotiated or voted on?— Shaba Nabi (@ShabaNabi) November 4, 2020
Is it to set us up as money grabbing GPs if we have capacity or liability concerns?@NikkiKF
An NHS England spokesperson said: 'The NHS has well established plans for delivering vaccinations across the country including the annual flu jab and children’s immunisations and work is underway to build on these tried and tested approaches, so that when a vaccine is ready, staff can deliver it safely.'