The children's home, St Joseph's, Enfield, was run by the Sisters of Charity of St Vincent de Paul (SVP) for the 'social service' arm of the Archdiocese of Westminster - “The Society of the Crusade of Rescue and Homes for Destitute Children”. It has already been pointed out that the records of such establishments have rarely survived. This is because about 1970 the attitude of society to the care of children in need was changing, from large institutions to smaller units, and then to fostering and adoption. The underlying philosophy had been that children in need should be encouraged to start a new life and leave their old one behind. One consequence of this was that records of their earlier life were not considered valuable, and so could be lost (think Windrush!). When it was later realised that people who had been in care or been adopted were helped by knowing of their background, the authorities gathered the surviving records as best they could. For Catholic homes, the diocesan children's services usually were the collectors of these records.
As Enfield is in the Archdiocese of Westminster, I would suggest that you contact the diocesan archive service. This service has a website at https://rcdow.org.uk/diocese/archives/ There are some helpful articles and there is a contact link.
This site suggests that there MIGHT be some records with the religious organisation, in this case the Sisters of Charity. They have a website at https://www.daughtersofcharity.org.uk/ and there is a contact link with a postal address and email address for their archives.
I think it unlikely that records of employment have survived, but if you do not ask you will not know.