Heather Watson’s defeat on Monday’s opening day of the US Open placed the hopes of British women’s tennis squarely on Johanna Konta and Laura Robson, a burden they shouldered with decidedly mixed results on a sweltering Tuesday afternoon in back-to-back matches on Court 11.

Konta, the British No2 who celebrated her run through last week’s qualifying draw with a hamburger from Shake Shack, continued her charmed summer form with a 6-3, 6-0 victory in exactly one hour over the American wildcard Louise Chirico. After breaking Chirico twice in early stages, Konta rallied from 0-40 down for five straight points to take the opening set. From there it was one-way traffic as the world No96 battered her outgunned opponent into submission from the baseline.

The surging Konta has won 14 straight matches since a first-round defeat to Maria Sharapova at Wimbledon, the longest uninterrupted run of success for a British woman in more than a decade. Twice Anne Keothavong strung together 14 wins in succession, in 2002 and 2005, but none of those came in grand slam play.

“I’m not counting,” said Konta, who was born in Sydney to Hungarian parents before switching allegiance to Great Britain three years ago. “To be honest it doesn’t make a different to how I feel when I step on the court. Every match I go out there to play is a new one. It doesn’t matter what’s happened before, what’s going to happen next. It really is about competing against the player you’ve got on that day.

“Trust me, they don’t care that I’ve won matched before or will win some later. We all start from zero when we step out on the court.”

Amid the form of her career, the 24-year-old attributes her purple patch to an increased focus on recovery and her work over the past year with mental coach Juan Coto, whose other clients include London hedge-fund managers and financial workers.

“To be honest I put it down to health. I’m lucky I’ve been healthy to compete as much as I wanted to and to keep going. I’m not taking that for granted. I’m very focused on doing the right things to recover well. I’ve got a great team around me.”

Konta advances to face the No9 seed, Garbiñe Muguruza. Konta will no doubt take heart knowing she prevailed in their most recent meeting at Eastbourne, just before the Spanish ingenue’s breakthrough run to the Wimbledon final.

The sticky environs of Court 11 were far less kind to Robson, who can take heart in her clearly restored fitness but little else after a 3-6, 6-3, 7-5 defeat to Russia’s Elena Vesnina – a match in which the former Wimbledon girls’ champion was at one juncture two points from victory, at 5-4 up and deuce in the final set.

“Any loss is tough but that one especially because, I mean if we’re being honest, I should have won,” Robson said. “That definitely makes it harder and makes me more determined to work harder for the next one.”

The former British No1, finding her way back into form after a wrist injury that sidelined her for 17 months and led to her dropping to No727 in the world, saved all four break points she faced in the opener and moved within a set of her first win at a major in two years.

Robson strung in five of her 12 double-faults during the second set as Vesnina levelled the score but she rebounded nicely early in the decider with a inspired mix of angled winners from both wings.

Yet with Robson serving at 5-5 in the third, she quickly fell behind triple break point before spraying a forehand wide. Within minutes Vesnina was through.

“I didn’t feel overly nervous,” Robson said. “I just took 5% off all my shots and that was enough to let her back into the match. She wasn’t going to give up. That 5% made all the difference and it didn’t work out.”

Now Robson will resume her comeback on the outer rim of the women’s tennis circuit, most immediately with a string of ITF events in Monterrey later this month.

“At the moment there are a couple Challengers in Mexico, so I’m going to take a lot of bottled water with me and hope for the best.” seven weeks agoin July, or Germany’s Carina Witthöeft in the next round.

Muguruza, ranked ninth in the world, would certainly provide a stern test but Konta is in the form of her life, having extended a winning streak whichthat now stands at 14 matches.

The 24-year-old Konta, the British No2, has always been a sound hitter from the baseline but she has previously struggled for both the power and mental toughness to succeed in the higher echelons of the gamemajor tournaments.

This, however, was an accomplished display on Court 11 and will give Konta confidence she can do more than just qualify for the main draws at grand slams.

She claimed two breaks in the opening set to lead Chirico 5-2 and while her opponent threatened a comeback with three break points, Konta held her nerve to serve out the set.

Buoyed by her advantage, Konta was more assertive in the second set, dictating the rallies and leaving a beleaguered Chirico powerless to respond.

Three breaks created a 5-0 advantage before a wayward backhand from the young American ensured Konta became the first British player in New York to make it into the second round at Flushing Meadows.