Mr Hancock, who was found to have been having an affair with aide Gina Coladangelo while lockdown restrictions were still in effect, announced his resignation from the post with a video on Twitter on Saturday evening.
The 42-year-old will remain as MP for West Suffolk, and will be replaced at the Department of Health by Sajid Javid.
MPs from across the political spectrum say this was the correct move.
Conservative MP for Portsmouth North, Penny Mordaunt, said: ‘[This was] the right decision.
‘Focus has to be on beating the virus and lifting the reamining restirctions safely.
‘Again I want to thank everyone who has been following the chief medical officer’s advice, often making immense personal sacrifices to do so.’
Fellow Conservative and Gosport MP, Caroline Dinenage, added: ‘I think it’s the right thing to do in the circumstances.’
But Labour MP for Portsmouth South, Stephen Morgan, believes the prime minister, Boris Johnson should have taken matters into his own hands.
He said: ‘Constituents have told me about how angry they are about recent revelations from this government.
‘Mr Hancock broke the law, breached the ministerial code and created serious conflict of interest questions.
‘His position as health secretary was untenable and it was a sign of weakness that Mr Johnson didn’t sack him.
‘The prime minister must ensure he appoints someone who will not waste taxpayers’ money, leave care homes exposed nor be accused of breaking government’s own Covid-19 rules.’
Mr Hancock wrote to Boris Johnson, informing the prime minister of his decision to step down over the weekend.
In the letter, the embattled MP said: ‘The last thing I would want is for my private life to distract attention from the single-minded focus that is leading up out of this crisis.
‘We owe it to people who have sacrificed so much in this pandemic to be honest when we have let them down as I have done by breaching the guidance.’
In response, the PM wrote: ‘You should leave office very proud of what you have achieved – not just in tackling the pandemic, but even before Covid-19 struck us.’
The government has since launched an investigation into how video footage of Mr Hancock’s affair, inside one of the government’s most secure buildings, was leaked.