Waiting for COA desicion, current visa expires. what to do?

Hi. I am in UK on HSMP visa which expires in 5 days.

I applied for COA 5 weeks ago, got a confirmation letter and no progress since. Does it mean I will be an overstayer and cant be married in UK if COA is granted after my HSMP expired? Or am I legally in UK while my COA apllication is under consideration? Technically, after COA granted, we need to place Notice to Marry and wait for 15 days, then marry, then I can apply for FLR(M). But my HSMP visa will be finished few weeks/months before I could apply for FLR(M).

My boyfriend is british. I know we should have considered marrige when we had time, but we were stupid.

Please help. Any info is appreciated.

YADP

Yet Another Duplicate Post.

now locked.