Britain's Andy Baddeley eased through to the semi-finals of the men's 1500m by finishing third in his heat.
Baddeley ran the first two laps at the back before moving through the field and finishing wide and fast.
Helen Clitheroe ran a personal best and new British record in the 3,000m steeplechase but missed the final by just over half a second.
Britain's Jenny Meadows and Marilyn Okoro qualified for the semi-finals of the women's 800m.
Meadows battled to third place in her heat, while Okoro looked particularly impressive as she came in second behind her heat winner Maria Mutola, who qualified fastest in one minute 58.91 seconds.
Jemma Simpson missed out after coming fourth in her heat.
Okoro, 27, revealed she was pleased with her performance but also admitted she was relieved to have got through the first round.
"I felt really relaxed out there, kept the nerves in check and tried not to do anything stupid and just bided my time," she said.
"I thought the gap wasn't going to appear and I was just squeezing through. I did get bumped and even drew blood (on a cut finger).
"The first round is dreadful for nerves so it is great to get it out of the way."
Baddeley, whose medal chances in the 1500m have been talked up by Sebastian Coe, was pleased with his first run.
"There is no outright favourite but at the moment I am only in the semis and there is a long way to go yet. I'm treating that as the next final so I am not looking any further ahead," he said.
"It felt good and I'm really pleased with that. There has been a lot of waiting and that has been quite nerve wracking, but once I got out there I felt really good."
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