Top seed Murray will take on world number 85 Edmund in the Aegon Championships quarter-finals at around 13:30 BST.
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“Obviously Kyle is the future of the game in this country”.
“I guess when you’re younger you can put up with it more, but as you get older it’s nice to have your own space and get that separation between work and chilling-out time”.
Edmund won eight of the nine points on his second serve, while Simon won just two of the 11 points in the third set when he missed his first delivery.
With Wimbledon just over a week away, Murray had one scare when he slipped on the wet grass and fell awkwardly but reported afterwards: “It was a bit of a shock at first but I’m fine”.
Four-time champion Murray will next face 2012 victor and fifth-seeded Marin Cilic after the Croat edged American Steve Johnson 6-7 (3), 6-3, 6-4.
Third-seeded Canadian Milos Raonic moved on with a 7-5, 7-6 (6) victory over Jiri Vesely of the Czech Republic.
“I haven’t got to play loads”, Murray said.
Top-seeded Murray struggled to gain the upper hand against his Davis Cup teammate, wasting an early break in the first set before breaking again to lead 4-3.
“I was a bit disappointed to lose the second (set), Kyle served extremely well there”. I know how well he can hit the ball when he has time.
Cilic, who was beaten by Murray in the final in 2013, saw off American Steve Johnson in his quarter-final match and aims to claim his second victory in the event following his triumph in 2012.
The 23-year-old will be in his first Queen’s semi-final after beating Luxembourg’s Gilles Muller 7-6 (7/5), 4-6, 6-2.
It was a thoroughly efficient performance from Murray in nearly wintry conditions that saw off the Slovenian-born player who moved to Britain eight years ago.
A first all-British quarterfinal at the Aegon Championships since the start of the Open Era was already guaranteed after Edmund’s second-round opponent Paul-Henri Mathieu pulled out with a wrist injury on Thursday morning ahead of their match. Murray’s frustration mounted as he failed to convert three break points in the next game and Cilic went on to level the match. Marin survived all of them, fending off the third with a attractive drop shot, and he brought the set home in game 10, forcing the deciding set.
“It’s very fortunate for me that he’s allowed me to come into his environment and shared stuff with his team”.
“It’s great all the British players are doing well”, Murray said.
Murray broke him for 2-1 but was then broken back himself when he served a weird, off balance double fault and then missed forehand wide.
Muller, who also reached the Queen’s quarter-finals a year ago, will face Australia’s Bernard Tomic, who beat Spain’s Fernando Verdasco 6-7 (2/7) 6-4, 6-4.
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Australian Bernard Tomic overcame Fernado Verdasco of Spain 6-7 (2), 6-4, 6-4.
