Incongruous is probably the most apt word to describe the scene: the last vestiges of December daylight are fading as the clock ticks past 4pm, yet the thermometer shows an on-court temperature close to 37C and perspiration is copious. Patrolling the baseline at the home of Britain’s Lawn Tennis Association, a sporting body that hasn’t been able to produce a female player worthy of a place in the world’s top 100 in almost a decade, is a young woman guaranteed to be ranked No 3 in the world after a week of 2008.

Critics of the LTA – and they are numerous given the paucity of British players at the top end of the world rankings – maintain that the £40m spent on the National Tennis Centre at Roehampton (complete with a thermostatically controlled climate system that allows the indoor courts to replicate the baking conditions of next month’s Australian Open) wasn’t intended to help Serbia’s Ana Ivanovic in her preparation.

Carl Maes, the LTA’s head of women’s tennis, maintained the presence of one the world’s leading players could only be a moti-vational and educational factor for British players. And though Ivanovic was given use of all the facilities free of charge, she was asked to spend time with Britain’s leading girls aged 14 and under to give them an insight into the competitive world some might experience in years to come.

“We can only gain from having somebody like Ana around,” said Maes, who coached the now retired Kim Clijsters from the junior ranks to a place in the world’s top five and remains confident of better times for the British cause, even though Andy Murray is the only player of either sex in the world’s top 100 at singles. “She is such an open girl who loves to talk but she also has that fierce determination to become the best in the world and the Eastern European work ethic. It was the perfect experience for our kids to interact and learn from one of the top players in the world. The policy at the National Training Centre is to welcome top-flight players from other countries because of the beneficial effect it can have on our players. Andy Roddick was here in the summer and Mary Pierce spent a few days training for a hopeful come-back a few weeks ago.”

Ivanovic, 20, who was forced to practise on the sloping tiles of a disused indoor swimming pool during her childhood as Nato aircraft bombed Belgrade, didn’t appear to be keeping anyone else from playing as she drilled balls with Anne Keothavong.

It wasn’t just the courts that impressed Ivanovic, who in the past year has earnt £1m in prize-money and spiralled up the world rankings to a year-ending spot of No 4 on the Sony Ericsson WTA Tour, a position that will definitely improve by one spot in the second week of January as her Serbian compatriot Jelena Jankovic has opted to play for her country in the Hopman Cup rather than the year-opening tournament in Auckland. “The facilities are just amazing, probably the best in the world, and the young British players are very lucky to have such a facility,” she said. “In designing this centre, it seems like they thought of everything. There is even this special pod, which is like a machine, that you can sit in to relax after training, and it speeds up the recovery time.”

After concluding her London preparation, Ivanovic headed back to Belgrade for a long sold-out celebratory exhibition match that also involved Jankovic and the nation’s two leading male players Novak Djokovic and Janko Tipsarevic. Before leaving, she added: “It is strange. We in Serbia now have two women players in the top four and Novak ranked third in the men’s game behind Federer and Nadal. And yet we can only dream about such luxury. There are plans for something in Belgrade but it will never be as special as this place that has everything.”

Everything but players. With the brothers Murray in Florida along with most of the nation’s junior hopefuls who will be heading for Melbourne in January, two neighbouring courts were deserted. Keothavong, now the nation’s No 2 after being overtaken by 125th-ranked Katie O’Brien, practised diligently in preparation for her bid to actually qualify for a Grand Slam rather than the charity of a wild card into Wimbledon while Naomi Cavaday, 18, nearly 2st lighter than when she almost beat Martina Hingis at this summer’s Championships, worked hard in the gymnasium.

Ivanovic appeared to utilise her 10 days at Roehampton well under the guidance of her own strength and conditioning coach, Scott Byrnes. Along with her teens, she also seems to have left behind the excess weight that forced some to question her long-term durability. She is a more honed and athletic figure than even six months ago, when she reached her first Grand Slam final at the French Open by pounding Maria Sharapova into early submission with the most forceful and focused of displays before her nerve deserted her against Justine Henin.

Knowledgeable observers within the WTA Tour expect her to flourish in the initial Australian tournaments and possibly overtake Svetlana Kuznetsova and become the world’s No 2 before the tour hits European clay in the spring. Aside from her French Open final, she won three titles in 2007 and reached the semi-finals of both Wimbledon and last month’s WTA Tour Championships in Madrid. Today she flies to Sydney to begin her warm weather training more than a month before the Australian Open begins on January 14, but Roehampton will remain very much in her mind.

“Living in Serbia is difficult for us players at the moment,” she said. “Firstly there are not good practice facilities, but also we have become so famous that it’s not really comfortable. I got almost mobbed by fans just trying to do some shopping in a supermarket. So I am looking for somewhere as a base and London is a distinct possibility. I love being in the city with all the things there are to do, transport connections are good to anywhere in the world and there is no better place to train.”

And with that she left, although not forgetting to settle her bill with the LTA; the price of a roll of tape used to cover a blister on her racket hand.