Miley finished fifth in her signature 400m medley event, in which she won silver at last year's World Championships, and advanced through the heats of the shorter distance in 2:12.27.
Chinese teenage sensation Ye Shiwen, who carved five seconds off her personal best to win the 400m medley in a world record, was the fastest qualifier while Miley was tenth quickest and British team-mate Sophie Allen, in her only Games swim, 21st.
"I'm happy with how that went, I'm just looking at this in stages and the semi was the first target," said Miley, after clocking 2:12.27.
"It's not my main event, I just feel more relaxed and happy now."
Allen, who won silver at the recent European Championships, admitted she was gutted with her display - and blamed her sluggish time and early exit on her equally early start.
"My aim was to make the final and I've not even made the semi - I'm totally gutted," she said, after touching home in 2:14.72.
"It's on par with my fastest ever heats swim, I always struggle to get into gear in the mornings but that can't be an excuse."
Three-time Olympian Caitlin McClatchey was seventh fastest into the 200m freestyle semi-finals but young team-mate Rebecca Turner didn't progress.
Turner swam a massive 1:57.68 personal best at the Olympic trials earlier this year but couldn't replicate that form on her return to the same pool.
She clocked 1:58.98 to finish 17th fastest, an agonising two hundredths outside a place in the top 16 and another swim.
"It was not my best race but I've got to keep looking forward," said Turner, who will now focus on the 4x200m freestyle relay.
"I don't think it went wrong particularly, it just wasn't really my day.
"We've all been training so hard and preparation couldn't be better, so that makes it more disappointing."
Joe Roebuck also missed out on progressing to the the semi-finals - again by the narrowest margin, just two hundredths of a second.
He clocked 1:56.99 in the 200m butterfly heats to rank 17th overall while Roberto Pavoni was 20th fastest in 1:57.55.
Both their times were over a second slower than they swam to book their Olympic places earlier this year.
"I'm very disappointed with my time. I wanted to go quicker, I wanted to get in that pool and swim a personal best at the Olympics and I thought I was in the shape to do that," said Roebuck.