Hancock made the statement when in a joint session of the Health and Social Care and the Science and Technology committees.
He said: “Why in Britain do we think it's acceptable to soldier on and go into work if you have flu symptoms or a runny nose, thus making your colleagues ill? I think that's something that is going to have to change.
"If you have, in future, flu-like symptoms, you should get a test for it and find out what's wrong with you, and if you need to stay at home to protect others, then you should stay at home.”
A recent report by insurance company Aviva, Embracing the Age of Ambiguity, found that heightened anxiety during the coronavirus pandemic has led to employees working longer hours and taking fewer sick days.
The percentage of employees that have taken zero sick days over a three-month period has risen from 67% in February, to 84% in August 2020.
Forty-three per cent of employees now describe their wellbeing as being less than good and 84% say that they would carry on working even if they felt unwell.
Research for the report was carried out in February 2020 and was repeated in August.
Paul Wilson, CMO, Aviva UK Life, savings and retirement, said: “The balance between work and home life; employment and retirement; and the relationship between employers and employees are becoming increasingly fluid. While some welcome flexibility, for many others it creates unease and uncertainty.”
The Trades Union Congress (TUC) has said that low sick pay in the UK is the main reason employees continue to work when sick.
The proportion of salary covered by statutory sick pay (SSP) is just 29% in the UK. Compared to Germany at 100%, Sweden at 64% and Spain at 42%.
For those who qualify, SSP is £95.85 a week, which the TUC said “is not enough to pay the bills” and would force four in 10 workers into financial hardship.
The TUC has urged the government to scrap the minimum earnings threshold for statutory sick pay; increase the weekly level of sick pay to £330 and give employers the resources to afford sick pay for their workers.