The UK Health Security Agency is urging all those eligible to get a vaccine to break the chain of transmission.
Public Health England figures show 179 cases of the Delta variant – first identified in India – had been recorded in Crawley by June 30.
That was 58 more than the 121 cases recorded the week before.
SEE ALSO Covid-19 vaccination walk in sessions in Crawley this weekend|Teens are using lemon juice and TikTok hacks to fake positive Covid tests to miss school | Crawley areas where Covid infections rose in the third week of June as ‘Freedom Day’ approaches | Face masks and social distancing could stay for next 5 years under Covid winter plan
Those identified in the latest week were among at least 12,892 cases of the variant recorded across the South East – the fourth-worst affected of England's nine regions.
The North West continued to have the highest numbers identified, with 55,936 Delta variant cases recorded there.
Across the UK, 50,824 more cases were recorded in the last week to reach a total of 161,981 – a 46% increase.
Of these, 42 are the so-called Delta plus variant, which India’s health ministry has said spreads more easily, binds more easily to lung cells and is potentially resistant to some drug therapy which can help neutralise the virus.
Three weeks ago, a total of 42,323 cases of the Delta variant had been identified in the UK, meaning the number has now increased almost four-fold.
But while the Delta variant now accounts for around 95% of new cases sequenced in the UK, the number of people being hospitalised with the infection is not rising proportionally.
Dr Jenny Harries, chief executive of the UK Health Security Agency, said: "The data suggest this is testament to the success of the vaccination programme so far and clearly demonstrates the importance of getting both doses of the vaccine.
"Come forward as soon as you are eligible. It will help us to break the chain of transmission, and it will save lives."
She added that the best thing people could do to protect themselves and loved ones from Covid-19 was to get the vaccine, if eligible, and get tested twice a week.
"Practice ‘hands, face, space, fresh air’ at all times," she said.
Of the 161,981 cases of the Delta variant recorded across the UK, 148,538 have been identified in England, 10,185 in Scotland, 1,749 in Wales and 1,509 in Northern Ireland.