Changing Employers on Tier 2 General

Hello guys,

I am a doctor working for the NHS.
My sponsor will be changing in Aug 2020. I am planning to apply for Tier 2 extension from within UK once I get my COS,which will be around May/June 2020. My current leave to remain expires In April 2023.

I have heard from a colleague that I need to start my new job within 28 days of receiving the new BRP but I havent been able to find that information anywhere. The tier 2 policy guidance says that I can continue to work for the previous employer until the start date on my new COS.

If I apply for a new BRP in June under Priority, Can I still work for my current employer on the New BRP since it will be an extension only and will include the dates I am supposedly working for my current employer?

I will be grateful for any clarifications.

Thank you

Regards
Ral