Ash Barty's incredible career-first in brutal Wimbledon thrashing

Looking unstoppable, Ashleigh Barty is on track to complete a rare Wimbledon title double after wowing British sporting royalty with a regal display to saunter into the second week for the first time.

Extending her winning streak to 15 matches, Barty overwhelmed British wildcard Harriet Dart 6-1 6-1 in a majestic centre-court debut as world No.1 on Saturday.

Olympic legends Sebastian Coe, Mo Farah and Chris Hoy, cricketers Joe Root, Jimmy Anderson, Jonny Bairstow, Eoin Morgan and Andrew Strauss and England football manager Gareth Southgate all enjoyed a Royal Box vantage point as Barty methodically picked Dart's game apart.

"It was incredible walking out there," Barty said of her 53-minute masterclass.

"A really special moment walking out onto court. One of the best tennis courts in the world. Privileged to be able to play on it."

But it was perhaps countryman Rod Laver, who was presented with a replica trophy before the match to recognise the 50th anniversary of his 1969 Wimbledon triumph, and fellow tennis legends Martina Navratilova and Billie-Jean King who would have most appreciated Barty's classic old-school performance.

Mixing mesmerising slices with exquisite drop shots, explosive forehand winners and 11 aces, Australia's relentless top seed wasted minimal energy or time in setting up a last-16 date on Monday with unseeded American Alison Riske.

"It was really good. I felt like I served really when I really needed to," Barty said after becoming the first Australian woman into the last 16 since Jarmila Groth in 2010.

"I tried to do as best as I could to get a quick start and then keep the ball rolling from there.

"I said to Harriet this will become your favourite court in the world. It's certainly mine."

Victory over Riske, the world No.55, would thrust Barty into a potentially mouth-watering quarter-final showdown with seven-times champion Serena Williams, who also advanced to the fourth round with a straight-sets win on Saturday.

Runner-up last year to Angelique Kerber, Williams beat German Julia Goerges 6-3 6-4 and will play Spanish veteran Carla Suarez Navarro in her 16th appearance in the fourth round.

Barty broke Dart on her first two service games to race to a 5-0 lead before pocketing the opening set with three booming aces.

There was no let-up for the French Open champion in the second set as Barty dropped just one more game in securing a commanding victory.

The 23-year-old received a standing ovation from Laver and the rest of the crowd after sealing her place in the fourth round for the first time in four visits to the All England Club.

"It's incredible to be here. It's a first for me. I've had a taste of it in doubles, but really excited to be here in singles for the first time," said the 2013 doubles runner-up and 2011 junior champion.

Barty is also through to the last 16 of the doubles after teaming with Victoria Azarenka for a 6-2 6-3 win over Rebecca Peterson and Timara Zidansek.

All up, Barty has won her past 28 sets in both formats as she continues her bold bid to join Williams and Lindsay Davenport as only the third woman in the past 20 years to claim both the Wimbledon singles and doubles crowns.

Barty is Australia's last hope in the singles, with John Millman losing his third-round men's match 7-6 (7-3) 7-6 (10-8) 6-3 to American Sam Querrey, a former semi-finalist.