Double amputee Whitehead improved his own T42 200m world record at the venue where he won Paralympic gold.
Visually-impaired sprinter Clegg, now racing in the T11 category, was in record-breaking form in her 200m event.
But Paralympic champion Jonnie Peacock lost out to American Jarryd Wallace.
Wallace won the battle of the amputee sprinters in the T44 100m with a time of 10.80 seconds to Peacock's 10.87.
There was also a defeat for wheelchair racer David Weir who finished third behind Swiss rival Marcel Hug and GB team-mate Richard Chiassaro in the T54 1500m.
But Rio-bound Hannah Cockroft (T34 100m), Jo Butterfield (F32/51 club throw) and Sophie Hahn (T38 100m) all recorded wins in their final big competition before the Games.
Listen: Whitehead smashes his own record
Whitehead, 40, was in blistering form, showing the benefits of the hard work he has done on his start to storm to victory in 23.03 seconds - beating his own mark of 23.46 set in Germany earlier this month.
"I wanted to be the first athlete to break a record on this track but Keni Harrison got there on Friday night," he told BBC Sport.
"Me and my coach Keith Antoine have worked on our race plan and I have put in a lot of start practice on the efficiency of my arms and legs.
"I worked so hard in the winter and I'm still in heavy training so I felt a bit tense at the back end but I ran a 22.69 in Newham this year and I want to get those sort of times in Rio."
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Commonwealth champion Clegg, 26, showed she will be a force in the T11 category if she is selected for her third Games in Rio, with a time of 24.44 seconds to win her event.
Clegg and new guide Chris Clarke are still developing their pairing and the Scot now has to run wearing a blindfold, as per the rules of her new category after she underwent medical tests in Germany last weekend which saw her move from the T12 class.
"I'm gobsmacked with that performance," she told BBC Sport. "We are getting better and better with every race.
"It's been a big learning curve for me and for Chris but I am loving every minute of it so far.
"The category change has been quite daunting because it means my sight has got worse and also running with a blindfold is different, especially with a new guide, so it's a lot of change all at once. But we have taken it in our stride and we are looking forward to the future.
"I want to be on that podium in Rio and in the T11 category my main rivals are Brazilian so that makes it interesting and exciting."
BBC pundit and 11-time Paralympic champion Baroness Tanni Grey-Thompson
The British team is in a really good place ahead of Rio and I was particularly impressed with T54 wheelchair racer Richard Chiassaro, who has made a huge jump this year.
I'm not sure David Weir did anything wrong but he still has plenty of time before the games and losing might give him an added incentive. However, for him, winning any medal in Rio will be great because of the strength in depth in that T54 category.
In the 100m, Hannah Cockroft has shown here that nobody can touch her and Sophie Hahn was another looking good for Rio.
For Jonnie Peacock, there is more to come from his start and more too in his finish. All of the injuries which have taken time out of training have hampered him and he maybe needs a few weeks more solid training.
Some of the psychology between him and American Richard Browne, which could be quite fractious, brought out the best of Jonnie. Jarryd Wallace is a different, more laid-back kind of character and maybe Jonnie needs a bit of that fire to bring out his best.
Richard Whitehead and Libby Clegg both set world records as Britain's Para-athletes warmed up for the Rio Games with some impressive displays at the IPC Grand Prix Final in London.