EEA2 relationship ending, need advise in informing HO.

[Sheba]

I have beening in this country nearly 12 years now.
Currently on EEA2 visa that expire in less than 2 years, not married.
But the problem is that after a painful break, me and my EEA partner deside to end the relationship, originially I wanted to leave the country becuase we were unhappy, but during the break I start to rebuild my life and wnated to stay now.
I think i can apply long reisidency ilr, but not sure how the process work,
On my visa i receive from HO, states i need to inform them when the relationship end.
So in terms of applying new visa, do I inform HO, then leave then apply entry clearance, then apply for ILR, or when i tell them, they let me apply for ILR straight away consider I do met the eligibility? Or do they give grace period for me to prepare my deparure or new visa application ? How does this work? Anyone had experience ?