It is 16 years since mixed doubles duo Jo Durie and Jeremy Bates became the last Britons to grace the roll call of Grand Slam winners.
Ask anyone who is most likely to end Britain's drought and the answer is simple, isn't it? It has to be Andy Murray.
Well, maybe not, because Jamie Murray could yet steal his brother's thunder and stake his claim to become Britain's next Grand Slam champion.
Andy (left) and Jamie Murray are close on and off the court
In a meteoric rise similar to that of his younger brother, Jamie, 21, has climbed from outside the top 200 to 43 in the world doubles rankings in less than a year, picking up ATP Tour titles in San Jose and Memphis along the way.
And while Andy battles to break Roger Federer and Rafael Nadal's stranglehold in singles, Jamie has chosen to operate exclusively in the more open doubles arena.
Top-ranked American doubles pairing Bob and Mike Bryan have won four of the last 13 Grand Slams, whereas in singles Federer has won nine and Nadal two.
So should British fans have a flutter on a Jamie Murray Grand Slam victory?
"It could be a good bet," agrees Jamie, who is surprisingly chipper for first thing in Miami. "And you'd probably get some good odds too!
"I've never thought about if I could win a Slam before Andy because either one of us could be first.
"Andy is bordering on the top 10 now so when the Grand Slams come round he is up there amongst the favourites, but in the doubles there is more scope for an upset.
How well Andy has been doing has helped inspire me to get to the level that he is playing at
"With Federer and Nadal, when he is on clay, it is more predictable whereas the doubles is more open. The Bryans have dominated but they still lose.
"They are losing more matches than Federer so there is always a chance and I'll be trying my best."
Born just 15 months apart, the Murray brothers' close relationship has helped fuel their rise the top of the British game.
Both were encouraged by mother Judy, a former Scottish national coach, to take up tennis at the same time, when Jamie was four and Andy three.
At the age of 12, Jamie left their Dunblane home for an LTA school in Cambridge, an experience which Andy later furiously claimed "ruined" his brother and convinced him not to make the same mistake.
JAMIE MURRAY FACTS
Born: 13/02/1986, Glasgow
Coach: Louis Cayer
Doubles ranking: British number one, World number 43
Titles: Memphis, San Jose, Dallas (Challenger)
Favourite surface: Grass & Clay
Other: Lives London, likes golf, supports Hibs
"It's not true that I was badly treated by the LTA," said Jamie, who admits the experience did disastrously weaken his forehand and leave him disillusioned.
"But what happened to me did influence Andy going to Spain (to train at Barcelona's Sanchez-Casal Academy). He did something different to other British players, it was the basis for him to find his game and it is paying off now."
In turn, Andy's confident rise to the cusp of the world's top 10 has now helped restore Jamie's enthusiasm.
The Scottish siblings try to compete at the same events as much as possible, are occasional doubles partners and Andy's coach Brad Gilbert is happy to share his advice.
When Andy won the singles title in San Jose and Jamie followed suit by claiming the doubles, Andy described it as "the proudest day of my life".
Gilbert and Andre Agassi (left) entertain the Murrays and Lloyd
"How well Andy has been doing has helped inspire me to get to the level that he is playing at week in week out," said Jamie, who also shares his younger brother's relaxed drawl.
"Brad helps me out quite a bit and comes to watch my matches. It's good to be able to look up and see Brad Gilbert cheering for you. It's motivating, that's for sure."
A joint Murray brothers Grand Slam is on hold for now while Andy concentrates on the singles, but Jamie plans to reap further rewards from his partnership with American Eric Butorac.
The two "lefties" first played together in Los Angeles in 2006 but became a serious double act - nicknamed "Stretch and Booty" by Gilbert - after the Australian Open.
"Eric and I are working out pretty good," said Murray. "We have good chemistry and plan to play for the rest of the season together.
"I want to get into the world top 10 and play in the Masters Series and the Grand Slams. I've started to get to that level, so it's exciting."
And what about the Grand Slam Murray v Murray wager? "I'll do my best," Jamie signs off with a laugh.