But for the first time in a generation, since the days of Virginia Wade and Sue Barker, Britain has two women players who are not only capable of upsetting the big names, but could also be good enough one day to compete for grand slam titles themselves.
Heather Watson and Laura Robson begin the year ranked inside the world's top 50 – Watson at 47 and Robson at 50 – and providing they can have a bit of luck with injuries, there is no reason why both should not be inside the top 20 come the end of the year.
Scotland's Elena Baltacha, who is due to return to the Tour in March after nine months out following surgery, had her share of good wins and made it to the third round in a number of grand slams but there was never really any expectation that she would go much further. Watson and Robson are different. Having each won a junior grand slam title – Robson at Wimbledon in 2008 and Watson at the US Open two years later – they were singled out for success early on.
Watson, 21 in May, became the first British woman since 1988 to win a WTA Tour title late last year. Robson, who celebrated her 19th birthday this week, has already reached the second week of a grand slam, at last year's US Open, where she beat Kim Clijsters and Li Na to make the last 16. She also made a WTA Tour final and picked up a mixed doubles silver medal at the Olympics, alongside Murray. Although both women receive financial support from the Lawn Tennis Association and train at the national academy in Roehampton, west London, neither is a product of the country's governing body.
Watson has trained at the Nick Bollettieri academy in Florida since she was 12. Robson has had a number of bases outside Britain and trained in Florida last month, working with Murray's fitness trainer, Jez Green, on her movement, an area of her game that had already shown vast improvement as growing pains eased and she grew into her near-six foot frame.
Watson is a sublime mover around the court and has admirable consistency but the consensus is that the more naturally powerful Robson is more likely to go further in the long run, aided also by being a left-hander.
Such astute judges as Martina Hingis, Tracy Austin and Martina Navratilova have all spotted Robson's talent and she loves the big occasion. It was a mark of her character that she was disappointed with her defeat by Sam Stosur, the defending champion, in the fourth round in New York last September. Robson genuinely felt she had a real chance of winning. The teenager was drawn in the same quarter of the draw yesterday as Serena Williams, who is seeded No.3 behind Maria Sharapova at two and the defending champion Victoria Azarenka.
Robson's first-round opponent is the American Melanie Oudin, whom she beat in the qualifying event this time last year. A repeat of that victory would set up a meeting with the former Wimbledon champion Petra Kvitova in round two, should the Czech defeat Francesca Schiavone.
While Green was putting Robson through some gruelling routines on court and in the gym in Florida, Watson, who opens against Romania's Alexandra Cadantu, was continuing to work on the area of her game that needs most improvement, adding power. Not blessed with Robson's height in a sport increasingly dominated by women who are 6ft-plus, it is a process she knows will take time, but one she is confident will pay off.
"I need to hit bigger shots and I've been working on that a lot, being more aggressive, coming to the net," she said. "Martina Hingis wasn't the biggest of girls. I'm going to make up for it [her lack of height] in other ways, with my movement and agility around the court, and also my mental toughness. With more experience in dealing with situations, and getting further into grand slams, I would really want to be in contention [to win one] within three to four years."
Watson had to pull out of the warm-up event in Hobart this week with a niggling elbow injury but she will be desperate to play in Melbourne, especially having gone into the event last year still in pain after spraining her ankle.
If either Watson or Robson, or indeed both, find themselves in the second week, it would not be a surprise. That's how far they have already come.