Tara Moore wasted two gilt-edged chances to reach Wimbledon's second round for the first time in a nervy three-set defeat to 2010 finalist Vera Zvonareva.
The British number five served for the match twice in the final set, only to spurn both chances and allow former world number one Zvonareva a much-needed victory as the Russian bids to rebuild her injury-hit career.
Moore relinquished her winning position to slip out 6-4 6-7 (7/3) 9-7, unable to edge home in a match that spanned two days, having been halted at one set all due to bad light on Tuesday.
Caroline Wozniacki also dashed British hopes to bring down Naomi Broady's Wimbledon campaign with a straight-sets victory.
The Dane backed up her run to the Eastbourne semi-finals by easing past wild card Broady 6-3 6-2.
Second seed Li Na had no problem with an early start as she breezed past Yvonne Meusburger in just over an hour on Court Two.
"I love to be the first match because you don't have to wait"
Some former Grand Slam winners would have been less than impressed to be placed on the outside show courts, but not the world number two.
"Yesterday when they showed the schedule for Centre Court and Court One on the TV, I said - go call the referee's office, maybe I will play first, at 11.30am. I love to be the first match because you don't have to wait," said 2014 Australian Open champion Li, who disposed of Austrian Meusburger 6-2 6-2.
"If they put you in fourth or last match, you have to wait for the match and for the whole day you couldn't do anything."
Na will take things as they come, aiming to go better than her three quarter-final appearances at the All England Club.
"It is easy to say, tough to do," she said of her own Wimbledon hopes.
Li will face Czech Barbora Zahlavova Strycova after she knocked out the 32nd-seeded Russian Elena Vesnina 6-4 6-2.
Number four seed Agnieszka Radwanska of Poland also moved safely into the third round as she recorded a straight-sets win over Australian Casey Dellacqua in the first match on Centre Court.
The 2012 Wimbledon runner-up won 6-4 6-0.
Five-time Wimbledon champion Venus Williams survived a scare to fend off the challenge of Japan's Kurumi Nara and come through 7-6 (7/4) 6-1 on Court Two.
The American will next face sixth seed Petra Kvitova after the Czech player, champion in 2011, won 6-2 6-0 against Germany's Mona Barthel.