The foundation of the Church building at Keynsham was laid by Bishop Lee on 16th March 1935 and the first Mass was celebrated on 20 October of the same year. Before that time local Catholics had to travel to Bath or Knowle, so in spite of the small numbers of Catholics in the area the Bishop decided that there should be a church in Keynsham.

The parish is indebted to the generosity of Edwin Marshall who left his money in trust: 'to have compassion on Catholics who are living at a distance from a place of worship'. The money was used to purchase a property for a price of £1280. There was some discussion about the dedication of the new church, and the name finally chosen was that of St Dunstan who had been Abbot of Glastonbury and later Archbishop of Canterbury. The first parish priest was Fr (later Canon) Michael Reidy.The central window on the west end of the church is by Angus and is a memorial to Canon Michael Reidy who served the parish for thirty-eight years. Windows at the side are by John Yeoman.

The church is close by the site of Keynsham Abbey, a foundation of Augustinian canons, established in 1170 - the year of the martydom of St Thomas of Canterbury. The Abbey was located below the present Anglican Church, to the east and at right angles to the bypass.

The initial phase of quiet growth was disturbed by the war and the evacuation of children who were in the care of the Sisters of Charity of St Vincent de Paul. Local Methodists lent rooms to be used as a school. The war years also brought to Corston the Poor Servants of the Mother of God who in 1940 established their novitiate at St Teresa's on a temporary basis during the London bombing From 1942 to 1952 it was a country annexe to St Mary's Hospital in Bristol, and then a convalescent home until 1958, when it became a nursing home for the care of the elderly. The sisters long association between Corston and Keynsham ended in 2006 when the sisters gave up the home.

Canon Reidy retired in 1973 and was succeeded by Fr Daniel O'Callagham who in turn, was succeeded by Fr Michael Larkin. Fr Larkin was succeeded by Fr Michael Fountaine in September 2004, who was replaced by Fr Tibor Szende in February 2015. Fr Matt Anscombe succeeded Fr Tibor in August 2019.

From 2004 the Parish Church underwent much renovation. A new lighting system sensitive to liturgical needs was installed by Smiths of Gloucester in 2006, followed by a complete internal redecoration. The stone altar has been recentred in the sanctuary and a larger ambo and new tabernacle added. The stations of the cross have been replaced with bronze castings from Italy. New statues of St Dunstan and Our Lady of Glastonbury were commissioned in 2007 from a well known Polish sculptor in Kracow and the same artist created a new processional crucifix (See image gallery). In 2007 a new Allen Renaissance Organ with acoustic portrait was installed in the the gallery, much enhancing the music as servant of the liturgy.

A mural of the tree of life was commissioned for the Sanctuary Wall by the American/Argentinian muralist Marcelo Lavalen in time for Easter 2009. The mysteries of the Old and New Testament are depicted in the form of birds in the Tree. In September 2009 Marcelo returned to England to paint a vibrant mural of Christ in Majesty in the Eastern Iconographic style (See gallery for photographs of the painting of the mural).

 In September 2013 a Baptismal Tryptych was installed by Marcelo Lavellen, the creator of our murals of the 'Tree of Life' and ‘Christ in Majesty’. A larger image of the tryptych and further details are available in the gallery.

Parish Details from 'The Diocese of Clifton' 1850 - 2000. by Canon J.A. Harding.