By the 1920s Mass was being celebrated regularly in private houses in Topsham by priests from Sacred Heart in Exeter.  When a former nonconformist chapel in Chapel Place came up for sale, Fr Barney from Sacred Heart bought it, and by 1930 Mass was celebrated there on Sundays.  However, Bishop Barrett did not think the surroundings were suitable for a permanent Catholic church and it was sold in 1932, when the new church of Blessed Sacrament in Heavitree, Exeter, was opened.  Topsham became part of Blessed Sacrament parish, and the dozen or so mass-goers went to Exeter by taxi.

Holy Cross parish was founded thanks to the initiative of Canon Thomas Cahill, who retired to Topsham at about this time, after a lifetime spent in Australia and New Zealand.  He contributed much of his life savings to the project.  The architect was Wilfred Mangan, and the builders were CC and WJ Turl of Topsham. 

The foundation stone was laid on the Feast of the Holy Cross, 14 September 1936, and the church blessed and opened on 11 February 1937.