Clitheroe and Twell were comfortable qualifiers for the 1500m final
England's Helen Clitheroe was the quickest of four home nations qualifiers for the women's 1500m final.
Scotland's Steph Twell and Clitheroe's team-mate Hannah England also went through while Northern Ireland's Ciara Mageean progressed as a fast loser.
England trio Conrad Williams, Robert Tobin and Graham Hedman all progressed to the 400m semi-finals.
However, Martyn Bernard, who won silver for England in Melbourne in 2006, crashed out of the high jump.
The 25-year-old from Wakefield, who won European Championships bronze in Barcelona in July and was a strong medal contender in Delhi, failed to reach the 2.16m qualifying standard for Saturday's final.
"Although 2.16 is just bread and butter, it just didn't happen," said Bernard.
"I'm just gutted. Qualifying is where you just want to go in and just get through.
"I was thinking about little niggles here and there. I had a little problem with my knee and so 2.16, I didn't really want to take it.
"I skipped the first attempt and I thought I would be able to get through with 2.13, but it wasn't the case.
"Then the next two attempts, I was just concentrating on my knee more than my technique and getting over it."
His team-mates Tom Parsons and Samson Oni were among 14 athletes to clear the height.
In the women's 1500m, Clitheroe, from Preston, clocked four minutes 09.34 secs in finishing second in heat one behind Kenya's Viola Kibiwott.
"I'm just delighted to be in the final in my fourth Commonwealth Games - for an old girl it's not bad," said the 36-year-old.
Clitheroe's team-mate Hannah England was fourth easing down in the second heat, in a time of 4:13.91 while Twell was also comfortable in finishing fourth in her heat in 4:10.35.
Kelly McNeice from Northern Ireland faded after setting the early pace in the second race, which saw a Kenyan one-two from Olympic champion Nancy Langat and Jelegat Irene, and missed out on a place in the final.
Williams won his 400m heat in 45.78 - the fastest qualifying time of the six heats - with Tobin second in his heat in 46.26 to progress and Hedman through as a fastest loser in 47.45.
Seven gold medals will be decided in the Jawaharlal Nehru Stadium on Thursday, including the men's and women's 100m titles.