Heather Watson, Naomi Broady and Aljaz Bedene all won their opening qualifying matches at the Internazionali BNL d'Italia but there was defeat for Laura Robson in Rome.
Robson, who gave a very encouraging performance against Victoria Azarenka in Madrid this week, had a tough draw against American Christina McHale and went down 6-4 6-2.
Third qualifying seed Watson was made to battle hard by Italian Nastassja Burnett but recovered from a break down in the decider to win 6-3 2-6 6-3 while Broady was an impressive 6-3 6-2 winner over Zheng Saisai.
In the men's event, British number two Bedene fought back from a set down to defeat Italian wild card Omar Giacalone 4-6 6-3 6-1.
All three British players must win one more match to join Andy Murray and Johanna Konta in the main draw.
Meanwhile, Kyle Edmund won the fifth Challenger title of his career with a 7-6 (7/2) 6-0 victory over Filip Krajinovic in the Italian capital.
Edmund is under pressure from Dan Evans, who will play his own Challenger final in Busan on Sunday, for the British number three spot.
The 21-year-old lost only one set all week to clinch his second title of the season after victory over Evans in Dallas in February.
Source: PA
