56 Church Road, Tranmere. The workhouse later became Birkenhead Municipal Hospital then, in recent times, was known as St Catherine's Community Hospital
There's a bit more info in a post on the Liverpool FHS Forum:"It had ceased to be a 'Workhouse' in the 19th and early 20th century tradition but continued to operate a Public Assistance Institution until the abolition of the Poor Laws in 1948. The Workhouse Infirmary had become the Birkenhead Union Infirmary until 1934, then it was known as the Birkenhead Municipal Hospital until 1948, and thereafter St. Catherine’s Hospital. "https://www.lswlfhs.org.uk/phpBB3/viewtopic.php?f=22&t=10626