The NHS opened bookings to about one million people on Saturday morning.
It comes as surge testing is being rolled out in North Tyneside and parts of west London affected by the variant first found in India.
Meanwhile, Germany says anyone arriving from the UK will have to quarantine for two weeks, amid concerns over the spread of the variant.
The variant – also known as B.1.617.2 – is responsible for the majority of new cases in pockets of England.
In areas like North Tyneside people are being urged to get tested amid a rise in cases linked to the variant. Two extra mobile testing units in North Shields and Wallsend opened on Saturday.
Wider surge testing is also being rolled out in the capital with Ealing, Hillingdon, Brent, Harrow and Hounslow. It will target secondary schools in the five boroughs and PCR tests will be offered to everyone else in the area who do not have any symptoms.
More than 43% of adults in England have now had both doses of the vaccine – meaning they have maximum protection from the virus.
Around 38 million people in the UK have now received their first dose of the jab – and 22.6 million second doses have been given.