Kyle Edmund can join them if he beats Gael Monfils on Thursday.
No one could question the players' commitment in what was an nearly gladiatorial contest; Konta's roar and Vekic's tears after the final point speaking volumes about what they had been through.
"I think I moved pretty well too".
Konta, 26, said: "I'm seeing it as I get to be still involved in the Championships".
Normally by day three of Wimbledon Andy Murray is the only British player left in the draw, but not this year! "I think both myself and Donna played very well", Konta said.
Konta delayed her post-match press conference by more than an hour to have an ice bath in an effort to speed up her recovery after playing in temperatures approaching 30C on Centre Court.
And if he, Alijaz Bedene, Jo Konta and Heather Watson succeed it would be the first time so many home players have reached the stage since 1975.
The champion confirmed that he and his wife were expecting another child on Sunday, telling a news conference: "We're both obviously very happy and looking forward to it".
Heather Watson has one of the biggest matches of her life first up on Centre Court as she takes on two-time Grand Slam champion Victoria Azarenka.
How will the Brits get on next? He clocked up his 850th career victory as he cruised through his first round match on Monday and next faces Donald Young of the United States, the world number 43, in the third match up on Centre Court. Nadal's most competitive-or least lopsided-affair on the red clay of Roland Garros was a 6-1, 6-4, 6-3 second-round rout of Robin Haase. I'm a fan of just the show itself.
A first set tiebreak would decide matters and neither player would hold through the first three points. However, the gangly Brown's unpredictable playing makes him a treacherous second round opponent.
"It's been one of my goals forever".
They are good friends, but had never played one another on the tour. Are players going to the court less than 100% fit?
Big-serving players often deliver epic encounters and Gilles Muller and Lukas Rosol were on hand to produce the latest marathon affair. "It's really fun that I'm able to go home and spend time with my son", she said.
The huge Croat is always a risky opponent; his big serve and old-fashioned game thrives on grass better than on any other surface. It was hard for me to return well as she served very well.
Regular change at the top of the organisation in recent years hasn't helped, but something needs to be done: it's been 40 years since Virginia Wade won Wimbledon, and that was Britain's last Grand Slam win on the women's side.