From:
https://www.british-history.ac.uk/report.aspx?compid=22986
The Magdalen Asylum And Mrs. Lloyd's Charity.
An association for the establishment of a Magdalen Asylum was formed in 1828 and premises in Islington were acquired in 1829. It was 'to be a temporary asylum for women, fallen into habits of vice, who profess themselves penitent'. A new site was bought at Rotton Park in 1861 and the new buildings opened in the following year.
By a deed of 1869 Mrs. Elmira Lloyd gave £2,000, the income to be used for the benefit of the inmates of the refuge and probationary ward of the home. In 1920 the Magdalen Home Trust amalgamated with the Association for the Rescue and Training of Young Women to form the Birmingham Association for Unmarried Mothers and their Babies, and the home (formerly known as Kirkholme) became, as Hope Lodge, the principal home of the new association. Hope Lodge was closed in 1954 but the work of the association continued, and by a Scheme of 1954 Mrs. Lloyd's charity was to be used for the benefit of poor, unmarried women of Birmingham before, during and immediately after childbirth.
I believe the property was in Vernon Road at its junction with, and opposite, Clarendon Road Edgbaston and as it backed onto the ground of the Midland Red bus company's works, when it closed the company bought it to use as their head office, replacing cramped accommodation over the Bearwood garage premises. Certainly when I worked for Midland Red and visited it, it had a very "Institutional" feel to it. I asked its history once and was told "It used to be a home for 'Fallen Ladies'".
It appears on an eary map I have as 'Magdalen House', which all fits.
When the Midland Red company was split up it was sold to the health authority, and as far as I know still stands.