The Cathedral Church of SS. Peter and Paul is the Roman Catholic cathedral of the city of Bristol (not to be confused with the Church of England Bristol Cathedral). Located in the Clifton area of the city, it is the seat and mother church of the Diocese of Clifton and is known as Clifton Cathedral. It has been a Grade II* Listed Building since 2000. A 2014 study noted it to be the only Catholic church built in the 1970s to have been Grade II* listed. It was the first cathedral built under new guidelines arising from the Second Vatican Council.

Prior to the Roman Catholic Relief Act 1791 (31 Geo. 3. c. 32), Roman Catholics in Britain were banned from having public places of worship, and simply being a Catholic priest or running a Catholic school was liable to punishment with life imprisonment. By the time of Catholic Emancipation, and the passing of the Roman Catholic Relief Act 1829, Roman Catholics in Bristol had established a number of local places of worship, some of them in private houses, and in Clifton by the discreet purchase, through a third party, of a plot of land known as 'Stoney Fields' in what is now Park Place, Clifton. In 1834, the construction of a church began there, but it was built on a challenging hillside site and had a history of problematic construction work, making work there difficult. Building stopped 1835, started again in 1843, stopped shortly after and the building lay abandoned until 1848 when a roof was placed on the half-completed building so that it could be used as a church. Two years later, in 1850, Clifton was made an episcopal see and the church became the Pro-Cathedral of the Holy Apostles (1850–1973), intended to act in this capacity until a more fitting cathedral church could be constructed.

The people of the ProCathedral parish had raised some £250,000 (1970) for restoration of the ProCathedral. However, with reports from the civil engineers in 1964 indicating that the ProCathedral site in Park Place was unsuitable, an anonymous group of local people added to this a donation of £450,000 (1970), on the condition that a new site was found.

From 1962 to 1965 the Second Vatican Council met in Rome, discussing the renewal of the Church in its relationship to the world. The council's decree on liturgical worship focused on the role of the people, with the bishop and their priests in the celebration of the Eucharist. This was to be a strong influence in the design of the new Cathedral and, when built, the cathedral would be the first worldwide to be designed following the new guidelines.

In 1965, architects were commissioned by the Bishop of Clifton, Rt Rev Joseph Rudderham to undertake the design of a new Cathedral on a different site in Clifton. The design was primarily by Ronald J. Weeks, working with Frederick S. Jennett and Antoni Poremba of the Percy Thomas Partnership. Although the firm had little experience in ecclesiastical architecture, Ronald Weeks had contributed a design to the competition for Liverpool Metropolitan Cathedral, and had worked on a new Catholic church in Machynlleth.

The design brief was for a 1,000-seat church, with the congregation grouped closely around the High Altar so that they should feel and be a part of the celebration of the Mass, in a building that would last 300 years. Ronald Weeks worked closely with the Church team to develop their ideas for the cathedral. 'We are sure that only...a close working relationship between Architect and Client can achieve the level of 'Architectural Seriousness' advanced by the New Liturgical Movement.' Although Weeks was not a Catholic, he thought that this was an advantage: 'It's surprising how much people take for granted. Not being Catholics we could ask all sorts of questions which appeared naïve – like – "What is an altar?", in which one would get conflicting answers... each question would lead to a discussion which in turn helped to banish pre-conceived notions so we could plan right from scratch.'

As Kulić puts it: 'The approach of Gibberd [at Liverpool] and Weeks were therefore quite different. Gibberd took on the role of art-architect in response to a lack of direction from the client. Weeks's role was more that of a coordinator of the client's requirements, weaving them into a hierarchical and meaningful whole...Weeks was more in tune with the collaborative sociological methods that had been adopted...in the immediate post-war period.'

Kulić, comparing the design to that of Liverpool Metropolitan Cathedral (completed 1967), said: 'Neither its bishop nor its architects appeared to wish to use architecture as a way of leaving a mark for posterity, as did both Heenon and Gibberd [at Liverpool]...Liverpool could be proved to be liturgically conservative and naïvely designed, while Clifton could be seen as a model of liturgically advanced and sophisticated planning...Weeks and the Clifton clergy...should be praised for their intimate and knowledgeable collaboration.'