A hospital trust has become the first in England to recruit a private company to provide maternity care.
The deal between NHS Wirral and One to One Midwifery followed a pilot scheme in the area that involved 200 women.
In the two weeks since the agreement was reached, about 10 mothers have chosen to have their babies delivered using the optional new service.
Unison said that "maternity services are far too important to be entrusted to unaccountable private companies".
'Undermine the NHS'
Women who choose the One to One service will be provided with a midwife to see them through antenatal care, the birth and postnatal care.
Midwives working for the company will be allowed to go into NHS hospitals to deliver the baby if the woman chooses a hospital birth.
Christina McAnea, Unison head of health, said: "Of course pregnant women want choice, but they want a genuine choice over whether to have their baby in hospital or at home.
"They don't want an artificial choice between different types of providers... in the interests of a free market ideology that wants to undermine the NHS."
A statement from NHS Wirral said: "NHS Wirral continues to contract with local hospital-based maternity services providers (Wirral Hospital's Trust, Liverpool Women's Hospital, Countess of Chester Hospital).
"Therefore, women are free to choose the type of service and location of birth which they feel best meets their needs."
'Impact upon jobs'
Jacque Gerrard, the Royal College of Midwives' (RCM) director for England, said: "The RCM is aware of the progress made by One to One as a maternity service provider, and we welcome it as an add-on service for choice for women.
"However, we have reservations regarding the impact upon jobs for midwives in the NHS.
"We have formed a professional relationship with One to One to gain recognition for our members, as they will be an alternative employer for midwives."
Joanne Parkington, founder and clinical director of One to One, said the company would "relieve the pressure on the existing NHS system and introduce a specialised service for teenagers and the most vulnerable".
One to One currently employs 28 people, including 20 midwives, and said it is in talks with other NHS trusts around England and Wales about providing some of their maternity services.