Both prizes were awarded at the Dezeen Awards ceremony in London last night.
The Interior Designer of the Year prize is awarded for "all-round design excellence over a body of work by an interior designer or studio that has been in business for more than 10 years", while the Emerging Interior Designer of the Year award is given for "all-round design excellence over a body of work by an interior designer or studio that has been in business for 10 years or less".
i29 was also shortlisted in the Civic and Cultural Project of the Year category, with its renovation of 18th-century buildings at the Princessehof National Museum of Ceramics Leeuwarden in the Netherlands.
Spacon & X won the Emerging Interior Designer of the Year award, with judges saying: "This studio addresses contemporary subjects in the design industry and beyond. Their designs are fun but not childish, and show a delightful use of colour."
The studio's name is an abbreviation of "spatial conversion and cross-functionalism". Based in Copenhagen, the multidisciplinary design studio is directed by architect Nikoline Dyrup Carlsen, scenographic designer and advertising producer Svend Jacob Pedersen, and architect and fashion designer Malene Hvidt.
The interior design studio award winners were announced alongside studio winners for architecture and design at the Dezeen Awards ceremony on 27 November 2018.
Winners received a hand-made trophy designed by Atelier NL.
See all winners at www.dezeen.com/awards/winners.