Edmund eased past British number two Cameron Norrie 6-2 6-2 on Wednesday, shortly after Evans had been similarly impressive in defeating France’s Pierre-Hugues Herbert 6-3 7-5.
Edmund, Britain’s highest-ranked men’s player, had to overcome a 50-minute break in play when 5-2 up in the opening set, owing to two spectators receiving medical treatment after falling ill.
A British player is therefore guaranteed to be involved in the final four on Friday, and just days before the start of Wimbledon, Edmund said: “I have moved on (physically, from the French Open). I’m feeling a lot better and happier with myself.
“I was better at Queen’s (last week) and I feel better this week. It’s good that I can sort of transition what I have been doing in practice onto the match court.
“I have not played a lot of matches, in terms of winning a lot of matches. The more I can get, the more momentum I can pick up, is just great for me and building on my game.
“Every time I play a match and come through it in a positive way, I like that. So it’s sort of another opportunity (on Thursday). But it will be a tricky match with Dan. It always is, and on grass, it’s probably his best surface.”
Asked of the potentially-distracting delay, Edmund responded: “There is not very much you can do.
“There’s no point fighting it. You have just got to allow the time to go by, however long it is, and just make sure when you come back out you’re ready.
“I was in a good position, anyway. So there was no need to over-analyse and get stressed up.”
Evans, 29, had showed signs of frustration when a break down in the second set against Herbert, Andy Murray’s doubles partner at Wimbledon.
He received a warning after throwing his racket at the ground, but recovered his momentum to secure victory in straight sets and continue his recent fine form.
Asked about the prospect of meeting Edmund, he responded: “It’s great. It’s good to see so many Brits in the main draw here, singles and doubles.
“Hopefully we will have a good match. I did a good job and I’m happy with my performance. I felt better. It’s good. I feel good. I’m happy with how the day went.”
Johanna Konta’s preparations for SW19 earlier suffered the blow of her missing out on a place in the quarter-finals by losing in straight sets to Tunisia’s Ons Jabeur.
The 14th seed was largely outclassed as she lost 6-3 6-2 against her impressive opponent, and will therefore head to Wimbledon having played only five grass-court matches.
Konta, 28, had had a promising clay-court season, and said: “I definitely feel I’m bringing the same sort of thought processes and the same ideas from the clay to the grass.
“This surface demands certain adjustments and adaptations. I definitely feel like I have been able to adjust well movement-wise and also accepting on what the majority of points look like on the grass versus the clay.”