Sajid Javid said the UK Health Security Agency had detected cases in Chelmsford, Essex, and in Nottingham.
He said the cases were linked and the two people were self-isolating alongside their households while more tests and contact tracing take place.
The new variant has also been identified in South Africa, Botswana, Belgium, Hong Kong and Israel.
Ten countries are now on the UK's travel red list meaning, from Sunday at 04:00 GMT, all arrivals will have to quarantine in a hotel for 10 days.
On Friday, the UK placed South Africa, Namibia, Zimbabwe, Botswana, Lesotho and Eswatini on the list.
sked about potential changes in Covid restrictions, Mr Javid said: "We will do whatever is necessary to protect the progress we have made as a country. We've come a long way since the summer and we keep all of this under review and if we need to take further action, we will."