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Dujardin, 30, set world records in winning the freestyle dressage and grand prix events last year.
The double Olympic and world champion will ride Uthopia instead of her usual horse Valegro in Wednesday's freestyle.
Brash, the first rider to complete the sport's grand slam, competes in the World Cup showjumping on 20 December.
Four members of the Whitaker family, John, Michael, Robert and William, are also set to compete during the week, while Ben Maher, another London 2012 gold medallist, seeks to defend his Grand Prix title on Monday, 21 December.
Wednesday 16 December
Live coverage of the World Cup dressage freestyle
Red Button, online & connected TV from 20:00 to 22:35 GMT
Thursday 17 December
Live coverage of the Olympia Puissance high-jump competition
Red Button, online & connected TV from 21:00 to 22:15 GMT
Sunday 20 December
Live coverage of the latest World Cup leg, plus highlights of the puissance high-jump competition
BBC Two, online & connected TV from 13:45 to 16:30 GMT
Monday 21 December
Live coverage including the Olympia Grand Prix
Red Button, online & connected TV from 18:45 to 22:25 GMT
Wednesday 23 December
Highlights of the week, including the Olympia Grand Prix
BBC Two HD, online & connected TV from 11:00 to 12:00 GMT
All programmes times subject to change
Olympic champions and world number ones Charlotte Dujardin and Scott Brash head the field at the London International Horse Show at Olympia on Tuesday.