Two doses of the current AstraZeneca vaccine only had a 10.4% efficacy against mild to moderate infections caused by the B.1.351 strain, a study published in March found.
The variant of concern shares mutations similar to those of other strains, which has caused fears that people who are given a dose of the AstraZeneca vaccine could be exposed to a number of variants.
However, two doses of the vaccine were found to be 60% effective against the Delta variant first identified in India and the company has not confirmed if it will change its jab for that strain.
AstraZeneca has said any new versions of its jab would need to first be approved for use by the UK’s medicines regulator.
New vaccines needed to ‘keep country safe’
The Health Secretary, in a speech delivered at the University of Oxford where the jab was developed, said: "There is yet more to do, the work isn't over yet - we're still procuring all the time, and planning what we need to keep this country safe, including new vaccines specifically targeted at variants of concern.
"I can tell you today that we've started commercial negotiations with AstraZeneca to secure a variant vaccine - future supplies of the Oxford/AstraZeneca vaccine that have been adapted to tackle the B.1.351 variant first identified in South Africa.
"Once again, we're leading the way and backing projects with potential, so we can keep our vaccination programme one step ahead of the virus and protect the progress that we've all made."
AstraZeneca said “more details” on the negotiations would be shared in due course.
The Beta variant caused widespread concern across the UK after clusters of it not linked to travel first emerged in the UK in January.
The discovery of the strain resulted in surge testing and enhanced contact tracing across the country.
Leading up to 19 May, more than 900 cases of the variant had been reported in the UK, which was a rise of 41 from the previous week, Public Health England data shows.
Pfizer has previously said there is no evidence its vaccine, which is another of the main jabs being administered in the UK, needs updating against current variants.