In this document page 98 (paragraph 23.9) it says:
The start date given on the CoS must be the date that the migrant is expected
to start working for you at the time the CoS is assigned.
If such start date for a Tier 2 (General) migrant is subsequently changed after
leave has been granted, it must be within 28 days from the later of:
• the date on which their entry clearance or leave to remain is granted
• the start date on their CoS (taking into account any changes to start date
properly reported before leave is granted)