The walkout had been due to start at 07:00 BST on Monday and last until Friday.
Father of a teenager who took her own life after viewing harmful content says plans appear to have been brought forward for a "political reason".
The new defence secretary tells the Sunday Telegraph he is determined to ensure the military gets "what they need".
A campaigner is calling on the government to resume investigations into alleged encounters.
The annual event marks the King's official birthday and features more than 1,400 members of the armed forces.