Question: Was Brentwood Cathedral or Bradford Cathedral known as the parish church of St Peter for most of it's history?

Context paragraphs:
Brentwood Cathedral: The Cathedral of St Mary and St Helen is the Roman Catholic cathedral in the English town of Brentwood, Essex.  It is the seat of the Diocese of Brentwood.

Sheffield Cathedral: The Cathedral Church of St Peter and St Paul, Sheffield, usually called simply Sheffield Cathedral, is the cathedral church for the Church of England diocese of Sheffield, England.  Originally a parish church, it was elevated to cathedral status when the diocese was created in 1914.  Sheffield Cathedral is one of five Grade I listed buildings in the city, along with Town Hall, Abbeydale Industrial Hamlet, and the parish churches at Ecclesfield and Bradfield.  It is located in the city centre on Church Street and served by Sheffield Supertram's Cathedral stop.  It is one of three stops to be served by all tram lines.

Judith Rose: Rose was educated at Sexey's Grammar School, Seale-Hayne College and the London Bible College.  After an earlier career in Agriculture she became a Parish Worker at Rodbourne Cheney Parish Church, in 1976.  She was ordained deaconess in 1976, and priest in 1984.  She was at St George, Leeds from 1973 to 1981; Chaplain at Bradford Cathedral from 1981 to 199585; Minister at St Paul's Parkwood, Gillingham from 1986 to 1990; Rural Dean of Gillingham from 1988 to 1990; Chaplain to the Bishop of Rochester from 1990 to 1995; and Archdeacon of Tonbridge from 1996 to 2002.

St Peter's Church, Edensor: St Peter’s Church, Edensor is a Grade I listed church in Edensor, Derbyshire.  St Peter's is the closest parish church in the Church of England to Chatsworth House, home of the Dukes of Devonshire, most of whom are buried in the churchyard.  St Peter’s Church, Edensor is in a joint parish with St Anne’s Church, Beeley.

Dean of Bradford: The Dean of Bradford is the head and chair of the chapter of canons, the ruling body of Bradford Cathedral.  The dean and chapter are based at the "Cathedral Church of St Peter" in Bradford.  Before 2000 the post was designated as a provost, which was then the equivalent of a dean at most English cathedrals.  The cathedral is one of three co-equal mother churches of the Diocese of Leeds and a seat of the Bishop of Leeds; until 2014 it was the mother church of the now-defunct Diocese of Bradford and as such the seat of the diocesan Bishop of Bradford.  The current dean is Jerry Lepine.

St Peter's Church, Duxford: St Peter's Church is a Church of England parish church in the village of Duxford in Cambridgeshire.  From medieval times until the 19th century it was one of two parish churches in the village (the other being St John's), but their two parishes were merged in 1874 and St Peter's is now the sole parish church for the village.  It has been Grade I listed since 1967.

Bradford Cathedral: Bradford Cathedral, full name Cathedral Church of St Peter and formerly Bradford Parish Church, is situated in the heart of Bradford in West Yorkshire, England, on a site used for Christian worship since the 8th century when missionaries based in Dewsbury evangelised the region.  For most of its history the building was the parish church of St Peter.

St Peter's Church, Bolton: St Peter's Church, Bolton-le-Moors, commonly known as Bolton Parish Church, is a Church of England parish church in Bolton, Greater Manchester, England.  The parish church, dedicated to St Peter, is an example of the Gothic Revival style.  The church is recorded in the National Heritage List for England as a Grade II* listed building, having been designated in 1974.  St Peter's is an active parish church in the Diocese of Manchester and is part of the Bolton deanery and Bolton archdeaconry.

Lancaster Cathedral: Lancaster Cathedral, also known as The Cathedral Church of St Peter and Saint Peter's Cathedral, is in St Peter's Road, Lancaster, Lancashire, England.  It was a Roman Catholic parish church until 1924, when it was elevated to the status of a cathedral.  It started as a mission church in 1798, and the present church was built on a different site in 1857–59.  It was designed by E. G. Paley in the Gothic Revival style.  In 1901 a baptistry was added by Austin and Paley, and the east end was reordered in 1995 by Francis Roberts.  The cathedral is in active use, arranging services, concerts and other events, and is open to visitors.  The building is recorded in the National Heritage List for England as a designated Grade II* listed building.

Klagenfurt Cathedral: The Cathedral and parish church of Saints Peter and Paul, also known as Klagenfurt Cathedral, is the cathedral of the Roman Catholic Diocese of Gurk-Klagenfurt and the main parish church of Klagenfurt.  It was built by Protestants and dedicated to the Holy Trinity in 1581, and was the largest Protestant church in Austria at that time.  The cathedral was commissioned by Christoph Windisch, Klagenfurt' s first mayor.  In 1600, during the Counter-Reformation, it was given to the Jesuits and rededicated to the Apostles Peter and Paul.  The church was razed to the ground by a fire and had to be rebuilt in 1724.  Bishop Franz Xaver von Salm-Reifferscheidt made it the cathedral of the Diocese of Gurk in 1787.

Supporting paragraphs: Brentwood Cathedral Bradford Cathedral
Answer: Bradford Cathedral