The health secretary the “highly concerning” mutation was yet more infectious than the new strain recently discovered and that two cases had been discovered.
Anyone who has been to South Africa must immediately quarantine and a travel ban has been introduced.
Speaking at the Downing Street briefing on Wednesday, Hancock said both cases of the new variant had been contacts of cases who had travelled to South Africa “over the past few weeks”.
He said: “This new variant is highly concerning because it is yet more transmissible and it appears to have mutated further than the new variant that has been discovered in the UK.”
Hancock said Porton Down was analysing the new variant.
He added: “We are incredibly grateful to the South African government for the rigour of their science and the openness and the transparency with which they have rightly acted as we did when we discovered a new variant here.”
More of the east and south-east of England will enter the toughest tier 4 lockdown on Boxing Day, Hancock also said.
Sussex, Oxfordshire, Suffolk, Norfolk and Cambridgeshire, all of Essex, Waverley in Surrey and Hampshire including Portsmouth and Southampton, excluding New Forest, will all be escalated to tier 4.
It means all non-essential shops, gyms and leisure facilities, hairdressers and salons, and hospitality venues will be closed. People are ordered to stay at home where possible.
Household mixing indoors is strictly prohibited and only one person can meet up with one other from a different household outdoors.
Travel is also restricted unless for essential work purposes, childcare or healthcare. Nobody can travel in or outside of tier 4 unless essential. No tier 4 resident can stay overnight away from their own home.
Bristol, Gloucestershire, Somerset including the North Somerset council area, Swindon, the Isle of Wight, the New Forest and Northamptonshire as well as Cheshire and Warrington will all be escalated to tier 3.
Cornwall and Herefordshire have seen sharply rising rates and will be added to tier 2, he said.