New Employer start date

Hi

I recently switched employer (Tier 2 General to SKW) with COS start date as 15th July, I got an approval email on 13th July and BRP today (26 July) with an issue date of 21th July. I'm confused as what my work start date with the new employer should be. Should it be 15th July (COS start date) or 21st July (Issue date on BRP) or the day I received BRP?

My understanding is your work start date with new employer can be any date on or after the date mentioned on approved CoS. You can also serve notice period for your previous employer beyond the start date on your CoS.