Dance GB is a collaboration between the UK's three national dance companies, Scottish Ballet, National Dance Company Wales, and English National Ballet. A new piece was commissioned for each company, and they are being performed together in a triple bill that opened in Glasgow in June then toured to Cardiff, before finishing in London as part of Big Dance 2012, four days of dance in the Old Royal Naval College, Greenwich, on 5-8 July. It is part of the Cultural Olympiad, effectively a dance version of Team GB, and frankly, it was so good that even this deeply Olympophobic reviewer was practically reconciled to the whole circus. Whatever happens with the regeneration of the East End, or a temporary resurgence in national pride, the Olympics have already left us a fine legacy by enabling these three companies to create such a high-class performance together.

Thursday night opened with English National Ballet performing And the Earth Shall Bear Again, contemporary Israeli choreographer Itzik Galili's response to piano music by John Cage. The dancers wore identical thigh-length black gauze shirts and were often lit from the side in a warm orange light that made a design feature of their rippling leg muscles. From their first moment on stage there was no doubting their physical presence and technical control. Galili's choreography was superb, fusing perfectly with Cage's insistent, percussive piano score to convey the irresistible power of raw dance. There were a few constantly recurring, striking motifs (thrown-out hips, developpés over 180 degrees), but the overriding impression was of fertile creativity, as patterns changed constantly, and the dancers, at once sinewy and sinuous, gave their all to a demanding, exhausting and exhilarating performance.

The second piece was Dream, choreographed by Christopher Bruce for National Dance Company Wales to Ravel's Boléro. The setting was something like a 1940s village sports day, and three men and five women in period costumes leaped, crawled, tumbled and slid their way through stylised versions of various Olympic (rowing, fencing, boxing) and less Olympic (egg-and-spoon, sack and three-legged racing) sports. Dream cleverly combined appealing music and costumes with the Blitz spirit trope which has always been the most effective stimulant of modern British patriotism, as well as the generalised nostalgia surrounding this year's Diamond Jubilee, and the sporting ideals of the London Olympics (both 2012 and 1948), making it a sure-fire crowd-pleaser. However, its popular appeal was backed up by wonderful, inventive choreography, performed with unreserved enthusiasm by NCDW's irrepressibly energetic and charming dancers. The audience response was enthusiastic and quite rightly: Dream left a broad smile on everyone's faces.

Rounding off the triple bill we had Scottish Ballet performing Run For It, set by Martin Lawrance to music by John Adams. In set and lighting it came closest to the London 2012 theme. The dancers were in blue athletic-style shorts and mesh leotards by Yumiko Takeshima and the set featured an overhead installation of inverted, blunt-ended pyramids by Martin Boyce which was lit successively red, white and blue. Scottish Ballet look stronger every time I see them: their rise to world-class company under Ashley Page's direction has been truly meteoric. Lawrance’s geometric choreography, inspired by the discus, pole vault and other Olympic events, demanded technical precision and the dancers came up to it flawlessly, indeed almost too flawlessly. Perhaps it was the blue-tinged lighting, however, or the fact that Adams' music was too spare, but Run For It seemed rather cold and rigid after the fluid exuberance of the first two pieces; Lawrance has done much more interesting work elsewhere.

These were very different pieces, but they went together brilliantly. The unifying theme was not, however, the Olympics, or British national togetherness, but the joy and power of good dance. There is nothing like seeing the best contemporary choreography performed by highly-skilled, classically-trained companies. The dancers from ENB and NCDW in particular looked like they were loving every moment, and all three companies threw all their energy into the performance. The audience loved it, and the carnival atmosphere was heightened by the location, a marquee in the grounds of the imposing Old Royal Naval College which, as well as raked rows of chairs, featured prom-style seating on the floor at the front, allowing the audience to get unusually close to the dancers. In the intervals, we wandered outside, enjoying a view of the river at dusk and the offerings of some dozen delicious food stalls, as well as a string quartet. If only all dance venues were as atmospheric, and if only all programmes were as exciting! It is most probably an Olympic one-off, but I for one would love to see it becoming an annual event: if this triple bill was anything to go by, few things could be better for the British dance scene.