I presume your ancestor was John Rhodes. I have the following, which I thought came from the Midland pubs site, but it does not seem to be there now, so either they have deleted it or it was from somewhere else:
Located close to the corner of Cheapside, this beer house can be traced to 1838 when John Rhodes was listed in an Aston ratebook living in a property owned by Elizabeth Penn. In the following year the beer retailer and fire iron maker was listed in Wrightson's trade directory for Birmingham.
The pub was named in honour of Prince Albert of Saxe-Coburg and Goth who became the Duke of Edinburgh after marrying Queen Victoria in 1840.
John Rhodes was succeeded by Samuel Leadbetter, another man that conducted two trades at this address. In the 1845 Post Office Directory he was listed as a manufacturer in Carpenters' Bits and Braces, Iron and Brass Ship Sail, Thimble and Malleable Iron Nail. Sounds like he was a busy bloke.
By 1852 Thomas Clift was selling ales at No.64 Birchall Street. He came from a family of shopkeepers in Deritend. He later moved to the Red Cow in Gooch Street.
In the 1861 census widow Hannah Evans was listed as the licensee of the Duke of Edinburgh. Born in Portsmouth, 49 year-old Hannah Evans was widowed after her husband lost his life serving on a coastguard vessel. Her sons William and Edward, both brassfounders, were born in Bristol. They had previously in lived the St. Paul's district of Bristol where Hannah had run an eating house.
Henry Swinfen arrived as the landlord in 1863. He had previously been the licensee of the Green Man on the Aston Road, where, in the 1860 Post Office Trade Directory, he was recorded as a "manufacturer of English and Foreign Weights of every description, all kinds of weights accurately adjusted [established 1817]." He continued to operate his brass weight-making business in Birchall Street along with operating the Duke of Edinburgh. His wife Elizabeth probably looked after the pub during the day and he would have served ales in the evening. However his listing, along with the record of Samuel Leadbetter, suggests that the beer house adjoined a substantial workshop building. By 1866 Henry Swinfen's Brassweight Manufactory was based in Darwin Street whilst he had moved to a house in Legge Street at Gosta Green.
William Grove was the licensee at the time of the 1871 census in which he was recorded as a 32 year-old Birmingham-born retail brewer, suggesting that homebrewed ales were produced on the premises. The Grove family were all Brummies. His wife Emma was two years younger. The couple had five children - Elizabeth, William, Harry, Florence and Thomas. They employed 44 year-old Emily Turvey as a general servant.
The Grove's soon moved to the Roebuck at Moor Street and were succeeded by former coal dealer William Pickersgill who came from the George and Dragon in Wharf Street. The Victorian age seems to be a period of musical pubs for many of the licensees of the town.
Evidence of home brewing was still in evidence at the Duke of Edinburgh in the 1880's. Charles Teale was the licensee at the time of the 1881 census in which he was listed as a retail brewer. He was born in Pershore in 1844. Two years younger, his wife Ann hailed from the Black Country town of Tipton. Their six children also lived at the pub. Five years later the family moved to the Manor Arms at Cato Street before taking over the Bull's Head in Villa Road where Lozells meets Handsworth.
Charles Teale was succeeded by Mary Ann Phillips who came from the Vine Inn at Blews Street West. Despite holding the licence of the pub, Walter Harley was recorded as "living on his own means" in the 1891 census. It was his wife Emma who was listed as publican and daughter Ann helped her run the place. The ratebook for the same year details the pub as a retail beer house with brewhouse, maltroom, workshop and premises. Still in Birchall Street but on the other side Cheapside was the maltroom, kiln and premises of Walter Thomas Kirkland.
The Holt Brewery Company had acquired the Duke of Edinburgh by the time the ratebook for Bordesley and Deritend was compiled in 1906. The annual rent for the property was £34.0s.0d. As manager John Hodgkins paid the rates of £4.19s.2d. on behalf of the Aston-based brewery.