The Conservatives and Labour have both included the plan in their manifestos ahead of 8 June's general election.
It comes after a petition started by Lucy Herd, from Sandhurst in Berkshire, accumulated 231,754 signatures.
Her 23-month-old son Jack drowned in a pond in 2010. His father returned to work three days after his death.
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A Liberal Democrat spokesman said they would also support bereavement leave.
Bereavement leave policies are not mentioned in the Green and UKIP manifestos, and the parties have not responded to an invitation to comment.
Ms Herd told the BBC that the lack of time to grieve contributed to the break-up of her relationship with Jack's father.
"No parent should have to bury their child and no parent should be expected to return to work within days of a death," she said.
Conservative Will Quince brought forward a private members bill for bereavement leave last year in wake of Ms Herd's campaign.
He said the manifesto promises now mean the policy will "almost certainly" become law, whichever party prevails after the election.
Ms Herd described this prospect as "tremendous" and "unbelievable" after seven years of campaigning.
Employees are currently entitled to a "reasonable" time away from work following a family death, but no statutory length has ever been set.
A grieving mother calling for parents to be entitled to statutory leave when their children die has welcomed cross-party support for the policy.