British wild card Ryan Peniston enjoyed a dream Wimbledon debut with Jack Draper, Alastair Gray, Katie Boulter, Liam Broady and Heather Watson joining him in the next round, but Dan Evans, Jay Clarke, Paul Jubb, Katie Swan and Sonay Kartal all bowed out.
Peniston is having a breakthrough summer after reaching the quarter-finals at Nottingham, Queen's and Eastbourne, and the 26-year-old continued his stunning form with a 6-4 6-3 6-2 victory on a packed Court 12.
He said: "To be honest, I was chatting with my coach, Mark Taylor, yesterday and I was kind of saying I'm waiting for someone to pinch me and wake up back in May sometime.
"I'm just loving every second of it, to be honest."
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The British No 6 from Southend will face American Steve Johnson, ranked 93 in the world, in round two after 18th seed Grigor Dimitrov retired from their match with a groin injury.
Peniston, who overcame a rare cancer as a baby, defeated French Open finalist Casper Ruud at Queen's in a stand-out win earlier this month and appears to have brought that form to the All England Club.
An impressive defensive performance saw the left-hander register just 18 unforced errors to Laaksonen's 44, while he secured six service breaks including one in the opening game.
The players exchanged breaks early in the third set before Peniston wrapped up victory with a further two breaks, punching the air in delight after a maiden Grand Slam win.
Draper hit a significant milestone at Wimbledon with what appears likely to be the first of many Grand Slam victories.
The 20-year-old has already risen more than 150 places in the rankings since taking a set off Novak Djokovic on his debut 12 months ago and he followed up his run to the semi-finals in Eastbourne to claim a 6-4 6-4 7-6 (7-4) victory over another in-form player in Belgian Zizou Bergs on Court 12.
British wild card Gray pulled off a remarkable straight-sets victory on his grand slam singles debut to reach the second round at Wimbledon.
Gray, ranked 288 in the world, saw off 2018 Wimbledon boys' singles champion Tseng Chun-hsin 6-3 6-3 7-6 (7-3) with a composed display on Court 14.
The 24-year-old from Twickenham, who attended the same US college as British No 1 Cameron Norrie, took the third set on a tie-break to potentially set up a clash with 11th seed Taylor Fritz in the next round.
Gray, the second lowest-ranked player in the men's draw, had won ITF World Tennis Tour events in Shrewsbury and Glasgow this year but had never played above Challenger Tour level.
Broady needed three hours and 30 minutes to down Lukas Klein in five sets.
World No 132 Broady, who made the junior final at the All England Club in 2011, recovered from being a break down in the decider to triumph 4-6 6-3 7-5 6-7 (2-7) 6-3.
It made the wild card the eighth Briton through to round two in the men's and women's singles and his reward is another meeting with Diego Schwartzman.
Schwartzman, who is seeded 12th, knocked out Broady in four sets last summer at the same stage.
Boulter became the sixth Briton to win on Tuesday and ninth to reach the second round in singles as she beat Clara Burel 7-5 6-3.
It was the third time she has made the second round at Wimbledon and one more win will see her post her best Grand Slam performance.
Watson booked her spot in the second round with a three-set win over Tamara Korpatsch.
The British No 4 was forced to come back to Court One after her match was suspended last night due to the local curfew tied at one set all.
But she finished the job in style on Tuesday, winning 6-7 (7-9) 7-5 6-2.
"These are the moments you dream of as a little girl," said an emotional Watson in her on-court interview. "I don't know why I'm getting emotional. I think I have had a really rough couple of years, like so many other people have. So this means a lot.
"I had a bit of a disaster match last year on this court, having match points. I really wanted to turn it around and win this year."
British No 8 Jubb was involved in a thrilling five-setter with Nick Kyrgios but could not pull off a shock as he suffered a 3-6 6-1 7-5 6-7 (3-7) 7-5 loss.
It took a mixture of big-serving and an array of glorious winners to send Kyrgios through after three hours and five minutes, with a sprinkle of trademark chatter with line judges and spectators thrown in for good measure.
After his victory, Kyrgios said in his on-court interview: "Incredibly tough. Obviously he's a local wild card, he had nothing to lose, played the moment and played some exceptional tennis.
"(The) crowd was pretty rowdy today, a couple of people in the crowd were not shy of criticising me. That one was for you. You know who you are.
"Obviously Wimbledon the last couple of years has been a strange one, a different feel, but it's special coming out here playing in front of full courts. Happy to be through and now just rest up."
British No 2 Evans crashed out in the first round in a surprise straight sets loss to Australian Jason Kubler.
Evans, seeded 28th, does not have a happy record at Wimbledon and that continued with a 6-1 6-4 6-3 loss to the Australian.
Swan won the first set against Ukraine's Marta Kostyuk but fell to a 4-6 6-4 6-4 defeat on Court 18.
The 23-year-old, making her fifth appearance at Wimbledon as a wild card, recovered from a difficult start to claim the opener in a hard-hitting battle against Kostyuk, ranked 76.
Swan, the world No 184 and British No 6, defeated Sloane Stephens in Germany last week and looked like she might pull off another significant win when she retrieved a break in the second set to make it 4-4.
But, having entered the court with heavy strapping on her left thigh, she began to noticeably wince, calling the trainer after dropping serve in the next game.
And, although there was little to choose between the pair until the end, Kostyuk held on to an early break in the decider to move through to the second round.
Clarke exited the tournament after he suffered a straight sets defeat to American qualifier Christian Harrison.
The duo resumed on Tuesday afternoon after their match was suspended late on Monday night, but only 15 minutes were needed on Court 18 before Harrison wrapped up a 7-6 (7-3) 6-1 7-6 (8-6) win against the British No 7.
Kartal did not benefit from her change of opponent as she went down to a three-set loss to Dutchwoman Pattinama Kerkhove.
The Brighton player had her chances but was beaten 6-4 3-6 6-1 on court 16.
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