The curator at the National Gallery could not contain her wonder. Calling me over to the replica of the Borgherini Chapel that has been installed as part of the gallery’s Michelangelo and Sebastiano exhibition, she pointed out a surreal detail. Not only has this reproduction of a piece of Renaissance architecture got hyperrealistic reproductions of the frescoes, marble decor and a half-domed alcove – it even has a modern plug socket sunk into the plaster.

That immaculate eye for detail is typical of the work of Factum Arte, a Madrid-based studio whose combination of digital analysis with assiduous craft is transforming the way we see art. I have been watching their work develop for nearly a decade. I am now convinced it is the most important thing happening in 21st-century art – because it can quite literally save civilisation.

The new kind of high-fidelity 3D reproduction being pioneered by Factum Arte is going to abolish the difference between past and present and make distance no obstacle to seeing any masterpiece. We are entering an age when museums can – this is no hyperbole – have their own perfect replicas of the Sistine Chapel, Titian’s Assumption in the Frari church from Venice, or Mantegna’s Camera degli Sposi from Mantua.

Facebook Twitter Pinterest Veronese’s Wedding at Cana, replicated by Factum Arte. Photograph: Factum Arte/Grégoire Dupond

The Victorian creators of the cast courts in London’s V&A would be amazed – and immediately commission all the above projects. These two vast galleries at the V&A are full of plaster casts of classical, medieval and Renaissance art and architecture. Michelangelo’s David, Hadrian’s Column and Ghiberti’s Gates of Paradise are among the wonders on view. Today we find this legacy of the Victorian passion for art history fascinating, yet we have the technology to go much further. A plaster cast of a Renaissance sculpture is only a pale copy compared with the hi-tech remakes pioneered by Factum Arte and a few other visionary enterprises such as the Insitute for Digital Archaeology, which put a replica of Palmyra’s Arch of Triumph in Trafalgar Square last year.

Facebook Twitter Pinterest Piranesi furniture recreated at Sir John Soane’s Museum. Photograph: Factum Arte/Alicia Guirao del Fresno

The first time I encountered this mesmerising new age of reproduction was in Milan in 2008. Factum Arte had made a facsimile of The Last Supper for an exhibition by Peter Greenaway. It was superbly convincing. Its founder Adam Lowe told me at the time about another project, in which he was remaking Veronese’s stupendously large painting The Wedding of Cana. Since then Factum Arte’s creations have got ever more impressive, from reproducing the tomb of Tutankhamun in Egypt’s Valley of the Kings to creating Piranesi’s fantasy furniture for an exhibition at the Soane Museum.

With the immaculate and freakily convincing simulacrum of Sebastiano del Piombo’s Borgherini Chapel for the National Gallery’s forthcoming exhibition, it is clear we are on the verge of a new age for art history: a renaissance of the Renaissance.

There is a chance to rediscover the magic of Renaissance art and architecture and popularise it as never before. The Borgherini Chapel is not even especially famous: visitors who climb the hill to the church of San Pietro in Montorio, above Rome’s river Tiber, where it can be found, usually go there to see Bramante’s compact architectural masterpiece the Tempietto in its courtyard. Yet by putting a loving and astonishingly real-seeming replica in the National Gallery, Factum Arte revives this work of art: our fascination with the reproductive technology inspires a fresh awe at the original it so passionately recreates. Far from creating some heartless museum of fakes for the post-truth age, this new kind of replica is a key to re-enchanting us with the art of the past.

Just as the Victorian age loved Michelangelo so much that people who could not get to Florence wanted to at least see a plaster cast of David at the V&A, or remind themselves of it between pilgrimages, so today’s feeling for art can be totally transformed by the combination of digital scanning, 3D printing and traditional craft that now makes it possible to reproduce art and architecture with such uncanny perfection, plug sockets and all.

A Sistine Chapel for every city – why not? Imagine if everyone in Britain had access to the marvels of the European Renaissance. It would change the way we see art, history and perhaps ourselves. For our loss of the passion for those achievements is a modern tragedy. A Sistine Chapel in Britain might have reminded us of what Europe really is when we voted on the EU last year.