Meanwhile, NHS England has confirmed that it will not move back the deadline for practices to opt in or out of the next phase of the vaccination campaign despite the potential impact of reduced supply on local vaccination sites' delivery plans.
Vaccination sites were told on 17 March to scale back plans for jabs beyond 29 March - after NHS officials confirmed a four-week slump in vaccine supply will 'significantly constrain' rollout.
Speaking in the House of Commons on 18 March, health and social care secretary Mr Hancock told MPs that a batch of 1.7m doses had been delayed because of a need to 're-test its stability'.
He said there had also been a delay in a scheduled arrival of vaccine from the Serum Institute of India, which is set to produce 1bn doses of the Oxford/AstraZeneca vaccine this year.
The statement comes just a day after NHS England wrote to vaccine sites to warn of a 'significant reduction in weekly supply available from manufacturers beginning in the week commencing 29 March, meaning volumes for first doses will be significantly constrained'.
Vaccination sites had previously been told that vaccine supply from 15 March would rise to double the level available in the first week of the month - and that this increased level would be 'sustained for several weeks'.
Mr Hancock said that despite the reduced supply, some first doses would be delivered in every week in April and second doses would be completed on time for around 12m people who were due to receive them.
Second-dose COVID-19 jabs
He told MPs: 'There will be no weeks in April with no first doses. There will be no cancelled appointments as a result of supply issues. Second doses will go ahead as planned.'
Assurances that some first doses will go ahead on top of second doses due in April suggest that supply overall will remain significant - and that vaccination sites will be delivering more doses per week than they have through the past five or six weeks.
The announcement of a drop in expected supply came as practices across England are weighing up whether to opt in to remain part of the vaccination programme beyond the initial nine priority cohorts identified by the JCVI.
Despite this, NHS England has confirmed to GPonline that the deadline for practices to sign up will not be extended.
COVID-19 enhanced service
Practices have until midnight on Friday to sign up to the updated COVID-19 vaccination enhanced service - and are expected to confirm details of workforce as part of their application. However, the NHS England letter that confirmed vaccine supplies would be reduced - and suggested that some staff may need to be stood down or redeployed as a result.
GPs had said even before the supply issue arose that they would have liked longer to decide whether to remain involved in the vaccine programme beyond cohorts 1-9.
The update on vaccine supply comes as practices work to maintain uptake amid doubts over the Oxford/AstraZeneca vaccine triggered by suspension of its rollout in several EU countries after blood clots in a small number of patients who had received it.
Speaking after Mr Hancock's statement, Labour shadow health secretary Jon Ashworth made a statement supporting the Oxford/AstraZeneca vaccine. He said he had been told that 'hundreds of people failed to show' for appointments at one major vaccination site.
The European Medicines Agency is expected to make a statement later today on the safety of the Oxford/AstraZeneca vaccine. It has already said that 'benefits of the AstraZeneca vaccine in preventing COVID-19, with its associated risk of hospitalisation and death, outweigh the risks of side effects'.
AstraZeneca has said that 'careful review of all available safety data of more than 17m people vaccinated in the EU and UK' with its vaccine 'has shown no evidence of an increased risk of pulmonary embolism, deep vein thrombosis (DVT) or thrombocytopenia, in any defined age group, gender, batch or in any particular country'.
The BMA and RCGP have backed the vaccine, and NHS England medical director for primary care Dr Nikki Kanani has called it 'safe and effective'.