Tim Henman, from whom Murray inherited the burden, says: "There's still far too big a void behind Andy. It's not acceptable when you've got the money to invest in the game and, after three days of Wimbledon, there is just Andy left. That would be very disappointing."
Disappointment had become so ingrained in the British tennis experience since the 1930s that Murray's victory at the US Open last year was greeted with understandable enthusiasm, but which some observers considered disproportionate to a single sporting triumph. It was tennis's 1966 World Cup moment, but will there be a similarly agonising longueur to follow?
We were returned to a Murray-free landscape at Roland Garros where, because the world No2 was resting his injured back, there was not a single British player left in the French Open after the early departure Laura Robson, Heather Watson and Elena Baltacha.
If Murray were to build on his historic achievement in New York by unshackling the final millstone and becoming the first British male to win Wimbledon since Fred Perry in 1936, the public response would raise expectations even further. It would also hand the Lawn Tennis Association a second dream scenario on which to build, one which would be criminal to waste.
Murray's win at Flushing Meadows seemed to pass in a magic moment, an opportunity not fully embraced, leaving emptiness similar to that which followed England's Ashes heroics of 2005. Still, there are signs the LTA recognise the depth of the stasis and they say they are about to do something about it. We will see.
Shortly after Wimbledon, they are expected to announce the name of a new chief executive. He or she will earn considerably less than the £640,000 a year the departing CEO Roger Draper was banking, with pensions and bonuses, towards the end of his seven-year tenure, and, with the support of an administration likely to be streamlined and operating under the sharp scrutiny of Sport England as well as an impatient public, that person will have a remit to build from the bottom rather than the top. That person, with the support of an administration likely to be streamlined and operating under the sharp scrutiny of Sport England as well as an impatient public, will have a remit to build from the bottom rather than the top.
The names mentioned include former players such as Mark Petchey, David Lloyd and Debbie Jevans, who would be an excellent choice but reluctant to leave her job as chief executive of England Rugby 2015, which she began only last October. Baroness Sue Campbell, the departing chair of UK Sport, is another possible candidate. It is almost certain, however, that the job is assigned already and awaits only a public announcement because of the notice a suitable candidate would have to give.
Whoever it is will face the most challenging job in British sport, as it not only will demand the delivery of at least some short-term results but long-term stability. Also, the job description is impossibly difficult to satisfy: someone who knows tennis and knows business. What British tennis really needs is someone who understands the culture of the sport in this country, both good and bad.
Draper, who last week ushered in the renewal of Aegon's sponsorship, will remain in the post until September. But there is muck to clear from the stables before then, as the LTA have to convince Sport England they can bring more players on to courts throughout the country or risk losing £10.3m funding. The ultimatum this week was a cutting accusation on the eve of Wimbledon.
The LTA, rather than concentrating on the grassroots, for many years invested too much soft money supporting players who became used to handouts, a strategy that has failed to produce a single player to join Murray at the business end of the world rankings.
They have shifted the emphasis over the past few years but the British experience, at elite and grassroots levels, does not compare favourably with other countries.
Great Britain have just 66 men and 27 women in the senior world rankings, behind the United States (125 and 111), Germany (109 and 51), France (132 and 58), Spain (92 and 32), Italy (91 and 56).
Lower down, it is a statistical forest of varied interpretation. Sport England's director, Phil Smith, says: "The track record of participation in tennis has been pretty poor." The LTA challenge this perception, and there is no question they have tried hard to improve participation with a wide range of community-based programmes.
And at least they have the prime minister onside. David Cameron, who played tennis at Eton, this week lent his weight to the schools programme run by the LTA and the Tennis Foundation, when children from four primary schools in the Olympic and Paralympic host boroughs tried out mini-tennis.
Cameron said at prime minister's question time: "I think we should commend the LTA for the work they are doing, to try and make tennis much more of a mass participation sport. I see it in the primary school my children go to where more tennis is being taught and played."
Johanna Konta, the British No3, said at the launch: "You only have to see smiles on the faces of the children to see how much fun they have with a racket in hand. I want to play my part in helping inspiring kids to get involved in tennis – a sport that means so much to me." She was supported by Greg Rusedski, the former British No1 who oversaw Great Britain's win in the Junior Davis Cup in 2011.
So, there is no shortage of fine words and goodwill. Another voice that remains upbeat in a more hands-on environment is that of Leon Smith, the Davis Cup captain and the head of men's tennis with the LTA. He has the confidence of Murray, as well, having coached him as a junior, and he has done a good job in getting the best out of some brittle talent in Davis Cup victories over the past two years.
The player that Smith, Murray and several other good judges agree has the best chance of making it is the 18-year-old Kyle Edmund, who has played well for months and lost in two tight sets to the world No16 Gilles Simon at Eastbourne this week.
"He's really good, and he's improving a lot," Smith says. "Last year when he got a wildcard for the [Wimbledon] quallies, he had just one ATP point and was ranked about 1,800. Since then he is up to 440, 450. He's played a lot of clay-court tennis to try to build his game, with longer points. He has played mostly in Spain and the US, where the Futures events are a bit tougher.
"He's turned down a couple of significant wildcards along the way – the Miami Masters series main draw, Chennai – so he could stick to his plan. That shows the character he has got. He has won a couple of Pro Series Futures titles in the last 12 months."
If those achievements sound modest, Smith recognises the size of the task in the modern game.
"One of the big things for him over the next few years will be continuing his physical stature. He has quite a good frame. It's important to keep working on range of movement, flexibility, agility, speed, power, to match what he's got genetically. It will be a key thing not to rush his schedule, although he has to play bigger events now."
And the next big event for Edmund is Wimbledon. On Friday, the teenage wildcard drew a daunting opponent in the first round, the 6ft 8in Pole Jerzy Janowicz, seeded 24 and on the sort of upward path Edmund aspires to.
"I think Kyle's ready for it," Smith says. "His main attribute is that he generates a lot of power. His forehand is a big weapon. He's been playing mostly outdoors and mostly on clay where he gets a lot of topspin on the ball. His backhand is very solid, technically it's superb. He's going to keep working on his serve so it becomes more of a weapon. He's definitely progressing faster than the others."
The others include Dan Evans, who has made big impressions this year in the Davis Cup against Russia and recently in Nottingham. He is not in the draw, though, having lost in the first round of the qualifying tournament at Roehampton.
Henman says: "You've got Kyle Edmund, Ollie Golding, Luke Bambridge and Liam Broady, those guys are doing a lot of good things and have got the right attitude. I expect some bigger and better things from them in the next couple of years and it's important because we need to fill that gap."
Whatever the flickering signs of promise and good intentions, for now the gap still yawns.
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