Court One is dominated by British players on day four with Boulter opening play at 13:00 against Dart.
The 27-year-olds were born just four days apart and Boulter says they “both know each other’s games inside out, back to front”.
Boulter has won both their meetings on the WTA Tour, including a tight three-set battle on her way to winning the Nottingham Open last month.
It is a meeting between the British number one and two with Dart, ranked 94th, saying her opponent has “been having an amazing year”.
They will be followed on court by their male equivalents, left-handers Draper and Norrie, with the former recently taking over as Britain’s leading player.
Draper, the 28th seed, said he has “huge respect for Cam” and was expecting an “incredibly tough” match.
The 22-year-old told BBC Sport: “He is one of these guys with incredible discipline and always treated me extremely well as a young player. Cam is someone who has really shown me the way.”
Draper won his first ATP Tour title on the grass in Stuttgart last month before beating Wimbledon champion Carlos Alcaraz at Queen’s. Norrie, 28, said the younger man was playing at an “unreal” level.
“I’m really going to have to play my best to have a chance with him. He’s really looking good,” Norrie added.
“We have practised with each other a lot, we’re good friends so it’s a shame we have to face each other this early but I’m looking forward to the match.”
