Commonwealth champion Claudia Fragapane qualified for four finals on her World Championships debut in Nanning, China.
The 16-year-old Briton, who won a record-equalling four gold medals for England at Glasgow 2014, will compete in the floor, vault and all-around finals.
She will also take part in Wednesday's team final after the six-strong British squad finished fourth in qualification.
"I was pretty pleased but hopefully there's more to come," she said.
The Bristol-based gymnast, who said her "life has changed" since success in Glasgow, recorded the sixth highest score in the floor and seventh highest score in the vault.
"It has been pretty hectic since the Commonwealths and the atmosphere here is big in a different way, but it's incredible," she said.
Ruby Harrold also made the all-around and uneven bars finals and is "drawing on all her strength" after a tough year which began with the European Championships in May.
"It's been really hard to keep peaking, but I can't wait to go out competing again," said Harrold, after securing the last place in the uneven bars final.
"I'm so proud to be part of this team and to come here and prove to the world that we can do those routines is amazing."
"That is the one final I really wanted and I did feel a bit more pressure for it," she told BBC Sport. "I played safe today, so hopefully in the final I can push on."
Beth Tweddle, who has now retired, remains the only British woman to win a medal at the World Championships.
Fragapane, Downie, Harrold, Hannah Whelan, Gabby Jupp and Kelly Simm will return for the women's team final on Wednesday.
They scored a combined total of 224.596 over four apparatus in qualification to finish behind USA (235,038), China (230.753) and Russia (228.135).
British men's head coach Eddie Van Hoof confirmed Dan Purvis and Nile Wilson will compete in the all-around final.
They qualified outright, but Commonwealth champion and team-mate Max Whitlock, who struggled on Friday, could have been awarded one of their berths.
"The trust that we have with the team is important and the boys who are in there have earned their places," Van Hoof told BBC Sport.
The men's squad, which won Olympic bronze at London 2012, are aiming to secure their first World Championships team medal in Tuesday's team final.