This charismatic Cuban is probably the only big dance name who could compete successfully with the Bolshoi Ballet now here in London. But then, for many years, Carlos Acosta has continuously shown persuasive pluck and daredevil tactics to his devoted audiences, many of whom are supporting him in his latest summer season programme at the Coliseum this week. In a scintillating evening that shows off his unique skills in some wonderful choreography, Acosta dances superbly, performing pieces he knows, which, like a sparkling diamond, show off his many still brilliant facets. Classical Selection makes for a night to remember and one to record for posterity.

Celebrating his recent 40th birthday, he has chosen to showcase thirteen extracts from works that have moulded both his career and his unique style since joining The Royal Ballet in 1998. In this two-and-a-half hour medley of classical pas de deux, taken from the ballets of some of the greatest 20th-century choreographers – Fokine, Ashton, Balanchine and MacMillan – he danced seven of them, often long and physically challenging. These were not the run-of-the-mill duets that usually fill gala performances. Rather, they showed full-blooded moments filled with intensity and drama that conjured up the context and characterizations of the ballets they came from. Acosta's stamina, bravura and physical output left his audience breathless but his toned, glistening body and rippling muscles showed he was well prepared physically as well as mentally for the mammoth task at hand.

The evening started low-key – and, after all the fireworks, ended that way too. Happily the mood was never stunted by countless curtain calls after each piece – no matter how exciting the dancers had been – so that the evening moved seamlessly, never losing momentum. As the curtain lifted, a spotlight fell on pianist Robert Clark, playing softly at the back of the stage as Acosta came on. Slowly he readied himself for his first piece, removing legwarmers, putting on shoes, then sitting quietly and mentally preparing. After putting on his military cap and cape he was ready for the role of Vershinin in the pas de deux from Winter Dreams, originally created by MacMillan in 1990 to show off the supersonic talents of the newly defected Irek Mukhamedov and sweet young Darcey Bussell. Dancing the role of Masha with Acosta was Marianela Núñez, the Royal's spirited principal ballerina, and each of them graphically showed the passionate intensity of their illicit affair and heartbreaking parting. Their next pairing was passion of a different kind, and they made an exotic couple in Scheherezade at the moment when chief concubine Zobeide opens the prison doors of the Golden Slave. Alluring and lithe, Núñez flaunted her beautiful body, preening herself aristocratically as she fuelled the fires of passion in Acosta's Slave. His panther-like movements and sudden fully stretched leaps conjured up his excitement and desire, yet was not sexually overt as seen in some performances. The two dancers are very musical, and in each of their dances together, they completely lost themselves in their reactions to each other.

In the famous flashy party piece from Diana and Actaeon, their unique talents were again on display. Núñez is fleet of foot and a steady balancer, and Acosta powerful and athletic. Naturally he does not reach the heights of his younger self – I first saw him dance this piece aged 18 – but he has a presence that transcends the fancy footwork of today's young dancers, and is far more persuasive in his presentation. Their final pairing was in Apollo, where purity and classicism blended and their technique was immaculate.

However, Núñez was not his only partner. Leanne Benjamin, newly retired from The Royal Ballet, danced a beautifully controlled and tender pas de deux from MacMillan's Requiem. Being petite, she wrapped herself around Acosta's bulky body with grace and ease. However, in the final scene from Mayerling, she threw herself at Acosta, grabbing his neck as he turned her around, then manipulated her into awkward moves in his role as her drug-ridden suicidal lover.

In the bedroom scene of Manon, Benjamin was coquettish and flirtatious with partner Nehemiah Kish, showing off her still superb technique in freedom of flight, fearless leaping and tiny, speedy bourées. Kish, handsome and elegantly dressed in white, was a good foil for all her teasings and showed high jumps and turns. He later performed Gloria, MacMillan's tribute to World War I, in which he partnered first soloist Melissa Hamilton. She had danced The Dying Swan in the first half with dignity and beauty and incredible wing-arms. Later, she released the uptight classical technique in Wheeldon's Tryst, where, with Eric Underwood, she swung her long legs past the six o'clock stretch and almost snapped in two with quick changes of direction. Three other young dancers made up the team, each showing finesse, neatness and panache. Ricardo Cervera and Yuhui Choe performed the slow movement from Ashton's Rhapsody (originally created for Mikhail Barishnikov), offering beautiful, fluid lines. Then Cervera changed pace and style to dance Balanchine's Rubies with Meaghan Grace Hinkis, a flashy, sparkly opportunity to show off.

Acosta ended the evening with fellow Cuban Miguel Altunaga's Memoria, a thoughtful contemporary solo that brought in elements of his background – street dancing, shoulder rolls, head stands and rhythm. Then he slowly returned to his original chair, towelled himself off, changed shoes, packed his dance bag and slowly left. The theatre erupted and the cheers and shouts must have travelled as far as Covent Garden. It was one of those nights – hurry and get a ticket. You'll never regret it.

Carlos Acosta — Classical Selection, at London ColiseumMargaret Willis reviews Carlos Acosta's Classical Selection at the London Coliseum.5