For this 18-year-old from Sydenham, receiving the British Athletic Federation award as Young Athlete of 1995 from Prince Philip was an entirely relaxed occasion - even if it was something of a trial for her proud parents.
"They were getting a bit hacked off about it," she said. "But I just saw it as a fun day. I go with the flow."
She brings the same attitude to bear to a career as a hurdler, which many respected observers within the sport believe can take her to the very top.
Her energies this season are focused on Sydney and the World Junior Championships, where she has a very good chance of winning the 100 metres hurdles title. However, it is the prospect of her return to the same city four years hence - for the 2000 Olympics - which has coaches and commentators smacking their lips in anticipation.
Judy Vernon, Britain's former Commonwealth high hurdles champion, has coached Natasha ever since she asked to join her training group four years ago.
"You don't come across someone like her very often, and I've coached a lot of people in the last 15 to 20 years. Natasha is the most talented of all the athletes I have dealt with."
Her laid-back attitude is a key part of her achievements since she began competing for Britain at senior level at the age of 15. However, unlike her height, her powerful build and her long legs, it is not something she was born with.
She recalls competing in the AAA Under-20 Championships for the first time, when she was given a message from one of the other runners in the field that she did not regard her as being any competition.
"I was really, really scared," she said. "I went round asking everybody: 'Who is this girl?' It was on my mind all through the warm-up. In the end I came fourth and the girl who had sent the message was eighth. I thought to myself: 'I should have saved my energy and I would have done even better'."
She resolved not to let herself get similarly affected again. "I have to be in a relaxed state. Even if it is a big competition, I have to say: 'This is just another race. These are just people'."
Although Danvers has only just turned 18, she has already had extensive top-level competition. Last year she competed in grand prix meetings at Linz and Crystal Palace, which is just five minutes' walk from her home. She was fifth in the national trials and became the only British female athlete to win an individual medal at the European Junior Championships with silver in the 100m hurdles.
This season she intends to reduce her best high-hurdles time from 13.45sec to around 13.20, but it is at 400m hurdles where Danvers is likely to make her greatest impact. She is already the British record holder for 300m hurdles, with 41.99sec.
"She's running faster than Sally Gunnell did at the same age," Vernon said. "Hopefully she will emulate Sally. Natasha has got a very long stride - she finds the hurdles in the 100m close together even now. And she can hurdle with either leg, which is something you must be able to do if you want to be good at 400m hurdles."
Danvers was encouraged to start in athletics by both parents, who were athletes in their own right. Her mother, Dorrett, was a high jumper and runner for Croydon Harriers, and her father, Donald, was a highly accomplished high hurdler for Herne Hill.
She often bumps into people now who tell her about her dad, and how good he might have become had circumstances been different. "Back then it was quite hard for black kids to succeed in athletics," she said. "He didn't have the support that I have had."
His daughter is living in another world. When she finishes her BTech course in Advanced Science at Bromley College this summer, she has the option of taking up an athletics scholarship at a prestigious American university.
If she takes up the place, she plans to develop the other major areas of interest in her life, namely modelling - she is already on the books of the Boss agency for work on an Olympic catalogue - and music. Danvers has already made demonstration tapes of songs written by herself and recorded with a group of friends.
But Danvers has not got to this point in her career without being single- minded, albeit in her consciously relaxed fashion. "It makes sense in a sort of twisted but logical way," she said. "Some people might think it is arrogance, but it is what works for me. If you don't believe in yourself, you are fighting a losing battle."
Vernon sees a lot of herself in Danvers. "When I was competing for Great Britain a lot of people were satisfied just to make the team, but I wanted to win as well. I think Natasha and I are the same in that respect.
"She has got a lot of work to do, and I am holding her back at the moment because she has only just turned 18. But she has got plenty of time. I know she will be world class."
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