N. F. S. Grundtvig (8 September 1783 - 2 September 1872) is not easily translated into another country's terms. He was a pastor, poet, historian, teacher and politician, he wrote or translated something like 1,500 hymns, and he is credited more than anyone with shaping how modern Danes think about being Danish. He is the ideological father of the folk high school, the institution that put adult education within reach of farmers' children. His hymns changed the sound of Danish church services outright, replacing the slow measures of orthodox Lutheranism with the work of national poets. Denmark decided he deserved a church, and settled the design by competition. Peder Vilhelm Jensen-Klint won it in 1913.

Jensen-Klint (21 June 1853 - 1 December 1930) came to architecture the long way round. He qualified as a building engineer in 1877, studied painting at the Royal Danish Academy without finishing, and worked as a mathematics teacher and a city engineer before committing to buildings full-time. What he brought to the commission was an obsessive study of ordinary Danish village churches - particularly the stepped-gable churches of Zealand - and of the brick trade that built them. The foundation was laid on 8 September 1921, Grundtvig's birthday. Construction ran mainly from 1921 to 1926, and the completed tower section was inaugurated in 1927 as the Tower Church while the rest waited. Jensen-Klint died in 1930. His son Kaare Klint, an architect himself, carried the work through to completion in 1940 - twenty-seven years after his father won the drawing.

Inside, the plan is straightforwardly Gothic: a long narrow nave, two side aisles, a small transept, columns rising to pointed arches, ribbed groin vaults overhead. The proportions are Gothic too - the triple-aisled hall church runs 76 metres end to end and 35 metres wide, with the nave ceiling 22 metres up. It seats 1,440, which puts it in the same class as Copenhagen Cathedral. What is not Gothic is everything else. There is no carving, no colour, no statuary, no gilding. There is only brick: some five million yellow bricks, the standard Danish building material, laid with a precision that the absence of decoration makes impossible to hide. Jensen-Klint took the stepped gable off the village churches and doubled its apex, and left it at that. The verticality that a medieval mason would have achieved with tracery is achieved here by stacking.

Jensen-Klint did not design a church so much as a setting for one. Working with Vilhelm Wittrup, Charles I. Schou and Georg Gossel, he laid out a group of buildings on either side called Pa Bjerget - On the Hill - containing the parish hall and apartments, built between 1924 and 1926 in the same yellow brick and the same idiom. They frame the church symmetrically and hold the eye on it. The approach completes the effect: a long tree-lined road runs up through Bispebjerg cemetery straight at the west front, a viewing axis of the sort the Baroque used to stage palaces. Arriving on foot along it, the facade grows in front of you for several hundred metres before you reach it.

For all its severity this remains a working parish church rather than a monument. It is open to visitors throughout the year, not merely at service times, and it is wheelchair accessible via a stair lift. The organ that the building resembles is really there, and in fact there are two: a Marcussen instrument of 14 stops installed on the north side in 1940, and a much larger western organ added in 1965 with 55 stops, whose biggest pipe is 32 feet long and weighs 425 kilograms. Recitals on it are regular, and hearing an organ inside a building shaped like an organ, in a hall with no soft surfaces anywhere, is the reason many people make the trip out to Bispebjerg. Reykjavik's Hallgrimskirkja, begun some years later, reaches for a comparable fusion of Gothic and modern - but Jensen-Klint got there first.