Employees at Waltham Forest Council are entitled to an extra week of leave for every week their premature baby spends in hospital before their due date.
Campaigners hope the scheme will put pressure on ministers to change maternity and paternity leave laws.
The government said the UK's maternity leave system was already one of the "most generous in the world".
The council believes it is the first employer in the UK to introduce such a policy.
When babies are born prematurely, parental leave starts the day after the birth.
'Precious bonding time'
Catriona Ogilvy spent the first months of her maternity leave at a neonatal ward hospital after her son, Samuel, was born 10 weeks early.
She said: "Mothers like me lose precious time to bond and experience higher levels of mental health difficulties following the trauma of neonatal intensive care.
"They need more time once their baby finally comes home before going back to work".
Mrs Ogilvy, who has since founded the charity The Smallest Things, said Waltham Forest Council's "brilliant" policy was beneficial for the employer, parents and babies alike.
The council said up to 14 of the 109 employees currently on maternity or paternity leave would have been eligible for extra time off under the new rules.
Waltham Forest councillor Clyde Loakes told the BBC's Woman's Hour: "We just want to give that extra bit of comfort and let that extra bit of stress out of what is a very difficult time for both fathers and mothers."
However, Mrs Ogilvy said there were thousands more families whose employers will not be so flexible.
She wants the law to be changed so that leave begins on the baby's due date.
Her petition has more than 140,000 signatures.
Mrs Ogilvy's local MP debated the issue in Parliament in 2016 but the second reading of his proposed bill was cancelled.
A spokesman from the Department for Business, Energy and Industrial Strategy said: "The UK's maternity system is one of the most generous in the world.
"While the current system strikes the right balance between the needs of new mums and business, we'd expect employers to give working parents who have premature babies the support they need."
Advice for employers on how to support staff members with premature babies was drawn up in 2017 at the government's request.
-reprinted from BBC News