Every member of Britain's five-man team reached an individual final for the first time in history at the European Gymnastics in Montpellier.
Dan Purvis suffered a night marred by food poisoning, then vaulted into a judge's lap by mistake, but recovered admirably to reach the floor final.
Purvis is joined by Kristian Thomas, who also made the vault final alongside Ruslan Panteleymonov.
Louis Smith and Max Whitlock will compete for gold on the pommel horse.
Smith and Hungarian rival Krisztian Berki, leading contenders for Olympic gold on the pommel horse this summer, each posted impressive 15.900 scores.
Britain's overall score of 265.718 sees them qualify in first place for Saturday's team final, also for the first time in history, ahead of Russia (264.474) and France (263.687).
It is unprecedented for every member of a British gymnastics team, male or female, to reach an individual final at a top-level senior European or world event.
Smith told BBC Radio 5 live: "The focus isn't at all on medals, it's about preparing in the right way for the Olympic Games in the summer. This is a good rehearsal in terms of atmosphere and pressure.
"All credit to Dan Purvis. He was ill all night with sickness and diarrhoea and this morning he looked like Casper the friendly ghost.
"He was an absolute hero, he really dug deep. He had a bit of a hurdle over the judge on the vault, but he was fantastic and the team pulled through. That vault zapped him into gear."
At this year's event there is a team final but no all-around final. Purvis finished the best-placed gymnast across all six pieces of apparatus in qualifying, despite his interrupted night and early mishap.
Purvis said: "I had a really bad night's sleep and was quite ill, so I didn't even know if I'd compete this morning.
"My team-mates, coaches and the physio were great and stuck by me, and that filled me with confidence and drive to carry on."
Dan Keatings, the world all-around silver medallist in 2009, is missing this event with ankle ligament damage but told the BBC this week that he will be fit for the Olympics.
Britain won the junior men's team title on Wednesday, defeating second-placed Russia by some distance.
Frank Baines, Brinn Bevan, Jay Thompson, Courtney Tulloch and Nile Wilson won Britain's second successive European junior team gold by a margin of 2.590 points.
"There's now a belief, I think because of Louis and Beth Tweddle, that we can do this. We're a good sport, a sport we're great at. In that respect, the kids are motivated and inspired," said GB junior coach Barry Collie.
"We've always had good juniors but definitely, in the last 10 years, we've become the best in Europe and started to challenge China and Japan. We're developing our own GB style and other countries are taking notice.
"My challenge now, for Rio 2016, is to get some of these kids on that senior team, to beat some of these current seniors."