We are on track for the opening on July 19 and we will watch vigilantly, we will look at the data in particular at the start of next week, Hancock told the BBC.
Hancock told Sky News that the government did want to let people have a family holiday, but only when it was safe to do so.
'After all, that's the whole objective of the vaccination programme, that's why it's so important that every adult goes out and gets the jab'.
Foreign destinations on the UK's amber list and whether they are open or closed to United Kingdom visitors.
Asked if vaccinated people get freedoms back by August and so enjoy a foreign holiday this year, Hancock said the government wanted to ensure safety but that he understood people wanted their freedoms back.
However, a member of the Scientific Advisory Group for Emergencies said the government should limit worldwide travel until amber list countries have their vaccination systems in place and their Covid-19 transmission reduced.
'We can now, all of us, see our vaccine status, see your testing status, on the NHS app, ' he said.
"You really don't want the virus being brought back from another country while we are doing our best to get levels as low as possible".
Jacqueline Dobson, president of the online agency Barrhead Travel, says millions of people in the industry have lost their jobs, and millions more fear for the future.
His remarks follow UK Prime Minister Boris Johnson indicating on Monday that things were "looking good" for July 19 to be the "terminus point" for England's coronavirus restrictions, even as he warned of a rough winter ahead.
Speaking during a visit to a laboratory in Hertfordshire, the PM said: "I want to stress that this is going to be - whatever happens - a hard year for travel".
Popular European holiday destinations for Britons, including Spain, Portugal, France, Italy and Greece, are now rated "amber", which require returning passengers to take three COVID-19 tests and isolate for 10 days on return.
The amber list includes some of the most popular summer hotspots such as Spain, Italy, France and Greece.
Additionally, the Media Minister, John Whittingdale, has said that more countries are set to be added to the green list by the end of this week.
The first "checkpoint" review since the traffic light system was introduced is due to take place on June 28.