Switch Employer - Transition process

[AliJaf]

Hello,

My 3 yrs SWV ends on 21 September, I am in talks with a new employer who is willing to wait 2 months and it looks promising that I may get the job, their already have a CoS which can be assigned anytime. I have asked for 2 year CoS to complete my 5 years

If I get the job;
I am confused how should I make this transition so that there is no loss of days due to transition and my ILR does not get impacted, due to few weeks overlap while switching, after end of year 5.

When should I apply to switch to new employer in terms of dates and when should I inform my existing employer (I am on 1 months notice) as I cannot control when and how they inform home office about cancelling my sponsorship.

Guidance please, thanks in advance