"Our focus is on keeping crucial air links open - bringing home the thousands of customers currently abroad, transporting vital goods, and ensuring people who are permitted to travel in and out of the UK for work, education and other reasons stipulated by the UK Government, can continue to do so," BA said in a statement.
BA said it would contact customers whose flights are cancelled to offer refund or rebooking options.
Sky News also reported that BA, part of the International Consolidated Airlines Group, would furlough more staff as a result of the changes.
Under new restrictions introduced in England on Thursday, overseas travel is permitted only for specific purposes such as work and study for the next four weeks.
The new boss of IAG warned last month he may have to strip even more costs from the business as a second wave of COVID-19 leaves its airlines staring at a bleak winter with very little travel.
(Reporting by Aakriti Bhalla in Bengaluru; Editing by Maju Samuel and David Evans)
