Anatasia's proud mum and dad Trudi, who is a volunteer receptionist at the hub and Alastair, who is a trustee, looked on with pride as the duchess smiled with delight as she cradled the baby girl.
But Prince William joked to delighted onlookers: "Don't be giving her ideas' before saying to his wife: "You can't take her with you."
The Royal couple have three children of their own Prince George (eight) Princess Charlotte, who is six, and three-year-old Prince Louis.
The touching moment came at the end of the Royal visit to the hub that was set up in 2019 by Pastor Mick Fleming to provide help and support for the homeless, vulnerable families and those struggling with mental health issues and addiction.
The Royal couple chatted with civic dignitaries, volunteers and service users during a tour of the hub which followed on from a visit to Clitheroe Community Hospital to champion mental wellbeing support given during the pandemic.