Cook set for Euro crunch.
Top breaststrokers Gibson (Loughborough University) and Cook qualified third and fourth fastest last night in their quickest swims of the year.
A return to form for Gibson saw him post a time of 60.74, while Cook, whose preparation was blighted by a groin injury, swam home in 60.85.
And Cook, winner of two gold medals at the Commonwealth Games before picking up the injury, was delighted, saying: "That was a great performance.
"To come through injury and swim that kind of time, especially in my longer event, is a real positive.
"It's down to a really good team of people that have helped me back to fitness."
Gibson added: "We're both faster than we were at Commonwealth Games. In fact, that's my fastest 100m for three years ( I feel like I'm getting back to where I was."
Britain's swimmers were kept off the rostrum on the opening night in Budapest as a series of records were broken.
Commonwealth champion David Carry (Loughborough University) made the final of the 400 metres freestyle where Russian Yury Prilukov took the gold medal.
"My aim was to get out quick as I felt I could come back quickly," said Carry. "It was very painful coming back down that last 100m.
"This meet is going to be much quicker than the Commonwealth Games. You have to race hard in the mornings just to make it through to the final and it showed tonight.
"I'm still very positive. It was a best time this morning and I'm learning all the time."
In the 400m individual medley, British record holder Becky Cooke (City of Glasgow) finished just half a second off her best for sixth, while 16-year-old Hannah Miley (Garioch) was seventh as gold went to Alessia Filippi of Italy. Cooke said: "I hope to step up from that later in the week. The IM (individual medley) is something I really enjoy but my main events are to come. I use the IM to vary my training, which helps me a lot."
Backstroke rivals Liam Tancock (Loughborough University) and Matt Clay (Swansea) have both made it through to the finals of the 100m event.
Tancock, whose training was put on hold earlier this year after suffering from a broken wrist, said: "I'm getting quicker all the time and I feel stronger every time I get into the pool.
"The wrist feels much better and I actually think it has given me more determination to succeed. I'm excited about tomorrow."
Clay said: "That was a better swim ( not far off my best and I put right what went wrong this morning. It looks good for the finals."
In the women's 200m backstroke, Loughborough University's Mel Marshall and 15-year-old Lizzie Simmonds (Lincoln Vulcans) both reached the finals.