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New legislation, known as "Jack's law", will come into force in April.
It means that parents who have lost a child will be entitled to two weeks' statutory paid leave from work.
But Unite assistant general secretary Diana Holland said this should be a "first step" in extending the same right to others.
She said: "Jack’s Law is a welcome first step in providing leave for people who have suffered a bereavement. Legislation must now be extended to include leave for those who have lost a close family member or are dealing with the grief of miscarriage.
"It is not enough to rely on the kindness of employers to ensure that people are given the time to process their loss.
"Bereaved workers are being forced to return to work before they have had even the semblance of a chance to recover, especially in industries where exploitative or insecure working practices are rife.
“Not only is this inhumane but for those working with heavy machinery or in hazardous environments it is a safety issue too.”
Lucy successfully campaigned for parents to get paid bereavement leave after the death of her son.
BBC Radio 4
Sarah Harris, director of bereavement support and education at the charity Child Bereavement UK, spoke to the BBC's Today programme about "Jack's law".
She said: "It's really helpful that there's now this statutory guidance in place to help support employers and their employees when they've been bereaved of a child.
"Being bereaved of someone important to you does impact on you. And people grieve very differently. This change in legislation will make a big change for parents going through the death of a child."
She also clarified that the two weeks' statutory leave bereaved parents in the UK will be entitled to from April will be paid.
BBC Radio 5 Live
Wake Up to Money
The new legislation will allow most working parents in the UK to take two weeks' statutory leave after the death of a child, the longest legal entitlement in the world.
It comes into force in April and it's named after Jack, who died just before his second birthday. His mother Lucy campaigned for a change for 10 years.
She told Wake Up to Money that previously, "there was no more than three days' leave, and any more time than that had to be taken as a holiday or sick leave. Obviously, the death of anybody is not a holiday.
"What I discovered as I shared my story was that more and more people came and told me they've experienced the same thing. Employers were telling them to take as much time as they wanted, but it would be down on their record as being off sick, and they'd then receive a P45.
"Something inside me had to make a positive out of a negative, and looking back, that is what got me through my grief journey."
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