Question: Which became a Cathedral first St Chad's Cathedral, Birmingham or Chelmsford Cathedral?

Passages:
The Bishop's House in Birmingham, England was designed by Augustus Pugin as the residence of Thomas Walsh, the first Roman Catholic Bishop of Birmingham.  It was situated opposite St Chad's Cathedral, on the corner of Bath Street and Weaman Street in Birmingham City Centre. Chelmsford Cathedral in the city of Chelmsford, Essex, England, is dedicated to St Mary the Virgin, St Peter and St Cedd.  It became a cathedral when the Anglican Diocese of Chelmsford was created in 1914 and is the seat of the Bishop of Chelmsford. The Dean of Chelmsford is the head ("primus inter pares" – first among equals) and chair of the Cathedral Chapter, the governing body of Chelmsford Cathedral, the Cathedral Church of St Mary the Virgin, St Peter and St Cedd.  Before 2000 the post was designated as a provost, which was then the equivalent of a dean at most English cathedrals.  The cathedral is the mother church of the Diocese of Chelmsford and seat of the Bishop of Chelmsford.  The Dean of Chelmsford is also responsible for the Chapel of St Peter-on-the-Wall at Bradwell-on-Sea, founded by St Cedd, among the oldest church buildings in regular use in England. Michael Leslie Yorke was an Anglican priest in the last decades of the 20th century and the first years of the 21st.  He was born on 25 March 1939 and educated at Midhurst Grammar School and Magdalene College, Cambridge.  Ordained in 1965 his first post was a curacy at Croydon Parish Church after which he served as Succentor, Precentor and Chaplain at Chelmsford Cathedral.  Following this he was Rector of Hadstock, a Canon Residentiary at Chelmsford Cathedral, Vicar of St Margaret’s with St Nicholas, King’s Lynn and Provost of Portsmouth Cathedral.  In 1999 he became Dean of Lichfield, and is now in retirement as Dean Emeritus. The Very Reverend Godwin Birchenough (27 October 1880, Macclesfield, Cheshire – 3 March, 1953) was the only son of Walter Edwin Birchenough and was the grandson of John Birchenough, a prominent Macclesfield silk manufacturer.  Godwin Birchenough, who was also a nephew of Sir Henry Birchenough, the President of the British South Africa Company, was educated at Rugby and Oriel College, Oxford.  Birchenough was ordained in 1905 and was Vicar of Moor Allerton between 1913 and 1921.  He became an honorary Canon of Chelmsford Cathedral in 1933 and in 1941 became Dean of Ripon Cathedral, becoming Dean Emeritus in 1951.  An eminent author, he was also vice chairman of the Additional Curates Society between 1934 and 1944.  Godwin Birchenough married Edith, daughter of Ernest Keay in 1912, he died on 3 March 1953. St Chad's College is a recognised (independent) college of Durham University in England, founded in 1904 as an Anglican hall for the training of Church of England clergy.  The main part of the college is located on the Bailey, occupying nine historic buildings at the east end of Durham Cathedral.  It neighbours Hatfield College to its north, while St John's College and St Cuthbert's Society are to its south.  The college is named after St Chad of Mercia, a 7th-century bishop. The Cathedral Church of Saint Philip is the Church of England cathedral and the seat of the Bishop of Birmingham.  Built as a parish church and consecrated in 1715, St Philip's became the cathedral of the newly formed Diocese of Birmingham in 1905.  St Philip's was built in the early 18th century in the Baroque style by Thomas Archer and is located on Colmore Row, Birmingham, England.  The cathedral is a Grade I listed building.  St Philip's is the third smallest cathedral in England after Derby and Chelmsford. The Very Rev Richard William Herrick (3 December 1913 - 5 May 1981) was an eminent Anglican priest in the 20th century.  He was educated at King Edward VI School Retford and Leeds University and was initially a civil servant.  He was ordained after a period of study at the College of the Resurrection, Mirfield in 1940.  he held curacies at Duston and Portsea, Portsmouth before being appointed Vicar of St Michael’s, Northampton in 1947, a post he held for a decade.  He was then a Canon Residentiary of Chelmsford Cathedral until 1978 when he was appointed Provost of Chelmsford.  He died in post. Gowing was educated at Fort Street High School and the University of Sydney; and ordained in 1907.  He began his career as a Curate at The Oaks, New South Wales, after which he served at Armidale Cathedral.  Coming to England he was on the staff of St James the Less, Bethnal Green then domestic chaplain to the Bishop of Chelmsford from 1914 to 1917.  He was vicar of Prittlewell from 1917 until his death; an honorary canon of Chelmsford Cathedral from 1921 to 1938 and Rural Dean of Canewdon from 1918 to 1938.  He was given the Freedom of the County Borough of Southend-on-Sea in 1953. The Metropolitan Cathedral Church and Basilica of Saint Chad is the mother church of the Archdiocese of Birmingham and province of the Catholic Church in Great Britain and is dedicated to Saint Chad of Mercia.  Built by Augustus Welby Pugin and substantially complete by 1841, St Chad's is one of the first four Catholic churches that were constructed after the English Reformation and raised to cathedral status in 1852.  It is one of only four minor basilicas in England (the others being Downside Abbey, the National Shrine of Our Lady at Walsingham and Corpus Christi Priory, this last now disused).  St Chad's is a Grade II* listed building.  The cathedral is located in a public greenspace near St Chad's Queensway, in central Birmingham.  s of 2014 the Archbishop was Bernard Longley and the Dean Canon Gerry Breen.

Supporting sentences:
The Metropolitan Cathedral Church and Basilica of Saint Chad is the mother church of the Archdiocese of Birmingham and province of the Catholic Church in Great Britain and is dedicated to Saint Chad of Mercia.  Built by Augustus Welby Pugin and substantially complete by 1841, St Chad's is one of the first four Catholic churches that were constructed after the English Reformation and raised to cathedral status in 1852. Chelmsford Cathedral in the city of Chelmsford, Essex, England, is dedicated to St Mary the Virgin, St Peter and St Cedd.  It became a cathedral when the Anglican Diocese of Chelmsford was created in 1914 and is the seat of the Bishop of Chelmsford.