This relates to the building of a type of particle accelerator called a synchrocyclotron by the Physics Department at Liverpool University, soon after the Second World War. At that time, these where the latest "big thing" in particle physics. And that was part of the problem. It was going to be too big to fit in the basement of the George Holt building which was, at that time, the physics laboratory. The basement housed a smaller cyclotron accelerator.
One of the major, very practical, problems concerned the radiation shielding of the machine. Whatever the material chosen, large amounts of it would be necessary and it would almost certainly also be in short supply. Rotblat's creative imagination worked again. Close to the university was a derelict piece of land that was earmarked for the new Metropolitan Catholic Cathedral. Although work had started on the crypt, the building had been stopped by the Vatican as the plans indicated that the new building would be larger than St Peter's in Rome [Aside: I haven't been able to verify the truth or otherwise of this reason for the halt to the building. The source relied on here, and in the biography of Chadwick quoted below, is an un-published MSc thesis on the design and construction of the Liverpool synchrocyclotron.] Walking the site, Rotblat realized that the sunken crypt and the ground topography would be a sginficant help in solving the radiation protection problem. The university Estates Department was instructed to open negotiations with the Catholic Church to try to secure a lease on the consecrated ground concerned. [John Finney "Joseph Rotblat: The Nuclear Physicist" in Joseph Rotblat: Visionary for Peace ed Braun, Hinde, et al; p.24]At the time of the planning and building of the Liverpool synchrocyclotron, the university's physics department was led by Sir James Chadwick, who had gained his Nobel Prize for discovering the neutron. According to Andrew Brown's biography of Chadwick:
There were major questions about the shielding necessary - how thick and what material - for radiation protection of personnel. One point was quite obvious: the synchrocyclotron would not fit into the basement of the George Holt Laboratory and a new site must be found. There was a derelict plot, partly cleared by the Luftwaffe, close to the university. For many years it had been the location of the workhouse, but in the 1930's was intended to be the site of the new Metropolitan Catholic Cathedral. Work had started on the crypt, but was interrupted when Archbishop Downey belatedly submitted Lutyen's blueprints to the Vatican for their approval. This was withheld when it was realized the new building would be larger than St Peter's, and construction came to a standstill. Walking over the triangular patch of land, Rotblat had the idea that the sunken crypt and slope of the gound would help solve the radiation protection problem. By December 1946, there was a scale map in the Physics Department, showing the enormous planned footprint of the cathedral and a small area in the southeast corner now earmarked for the nuclear physics laboratory. The land was consecrated, and the University Estates Department were instructed to enter negotiations with the Catholic Church with a view to obtaining a lease. [Andrew Brown, The Neutron and the Bomb: A Biography of Sir James Chadwick pp.329-330]Chadwick left Liverpool to take up a post in Cambridge before the synchrocyclotron was installed, so Andrew Brown's biography did not enable me to confirm that the crypt to Liverpool Cathedral did at one time house a leading edge particle accelerator.
However, to celebrate Liverpool's year as European Capital of Culture in 2008, the Institute of Physics prepared a guided walk, visiting places of scientific interest in the city. And, yes, they included the steps of Liverpool's Catholic Cathedral recognising it as the location of the synchrocyclotron. You need to go here, and your places of interest are no.3 (Sir Joseph Rotblat is the Rotblat being referred to in the two quotations above); no. 4 (though the heading is incorrect, and should refer to the site of the Liverpool synchrocyclotron, the cyclotron being the earlier accelerator in the basement of the George Holt Laboratory); and no.10 (which was the location of the physics department in Chadwick's time - ignore no.2 which is of more recent orign). The synchrocyclotron appears to have begun operating in 1955, though I do not know when it ceased operation.