Princess Anne, the Duke of Edinburgh, husband Mike Tindall and the entire population of Sevenoaks were at Greenwich to see Zara Phillips' Olympic entrance on High Kingdom, and the Regal One did not disappoint, posting a score of 46.10 penalties in the dressage that currently puts her in the top 10. By the end of the day she should be in the top 20, with most of the big guns in the competition riding later on Sunday.

The enthusiasm of the crowd had to be hushed as she entered the arena – the precision of the set movements means dressage horses must be kept super-chilled – but the flag-wavers managed to keep still for the five minutes of the test. The only sound was the gentle pop backing track – Robbie Williams' She's The One. The music at Greenwich is wittily chosen, with Blur's Parklife and the Rolling Stones' Wild Horses especially amusing. The last thing you want in dressage is a wild horse.

After her test Zara was immediately mobbed by the press, and there was a funny moment when the Swedish rider Sara Algotsson Ostholt overtook Zara in the interview queue and was mistaken for her by one of the press agencies. Attractive blonde women in top hats look remarkably similar. Algotsson Ostholt, who rode immediately after Phillips and had just gone into the lead in the competition, took the confusion in good heart. The non-royally connected riders at Greenwich know their place.

Phillips, whose previous Olympic hopes in 2004 and 2008 were dashed by injury to her world championship-winning horse Toytown, said she was delighted to at last be competing in the Games. "It was incredible to be selected," she said, "and to be here at home for the Olympics is an amazing feeling."

Her test went well except for one or two blips in the middle of the routine, when the horse laboured in a couple of transitions. "His first change was disappointing," she said, "but his other ones were really good. He coped well with the crowd, and he is only getting better. He's very chilled and getting stronger all the time."

Phillips will next be seen in Monday afternoon's cross-country phase, when the younger royals are likely to be in attendance. She said she was looking forward to tackling Sue Benson's twisty and testing course: "He's a good jumper and cross-country is his strongest phase. He is quick and easy to turn, so it will hopefully be good. I think he wants to get out there now. He's a bit bored of dressage."

Team GB are well placed as this phase of the eventing nears its conclusion, but Australia, Germany and the US are also performing strongly, and a medal is by no means guaranteed. Germany are traditionally very strong in dressage, so if the British riders can hang on to their elegant coat-tails today they will be well-satisfied as they go into the cross-country and the decisive show-jumping phase.