Kyle Edmund beat compatriot Cameron Norrie to set up an all-British encounter against Dan Evans in the Eastbourne quarter-finals.
The British number one beat the British number two 6-2 6-2 in a match suspended for around 50 minutes when a spectator fell ill.
Evans put in a determined display to beat Pierre-Hugues Herbert 6-3 7-5.
Top seed Guido Pella, the Argentine world number 26, lost 6-4 3-6 6-4 to American Taylor Fritz.
With Wimbledon starting on Monday, Edmund and Evans will be pleased to be getting more match time on grass.
Evans, in particular, heads to the grass-court Grand Slam in good form after winning titles at Surbiton and Nottingham on the surface this month.
Against Herbert – who will be British former world number one Andy Murray’s doubles partner at Wimbledon – Evans fought back from a break down in the second set to win.
He shouted “that’s woeful tennis” at himself before going on to celebrate victory with a loud roar.
Meanwhile, Edmund’s victory against Norrie was never in doubt with the third seed dominating from the start, breaking in Norrie’s second service game.
Play was suspended at 5-2 in the first set, with the players staying on court while a medical incident was tended to in the stands.
When the match resumed Edmund wasted no time taking the first set on Norrie’s serve.
He broke again early in the second set, and did not face a single break point in that set on his way to victory.
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Elsewhere, Britain’s Liam Broady is one win away from the Wimbledon main draw after beating Dutchman Tallon Griekspoor 6-4 6-7 (2-7) 6-2.
He faces France’s Gregoire Barrere, who is ranked 170 places higher at 117 in the world, in the final qualifying round on Thursday.
In women’s qualifying, Samantha Murray advanced with a 7-6 (7-4) 6-4 win over Spaniard Cristina Bucsa, but fellow Briton Gabriella Taylor lost 6-4 7-6 (7-5) to Belgium’s Ysaline Bonaventure.
The Wimbledon draw takes place on Friday at 10:00 BST.