travelling to home country without BRP

Hi,

I have lost my brp but need to travel to my home country (India). I am on a student visa and I lost my brp few days back (3rd october). I want to visit India for 2 weeks from 18th October to 3rd November. I have applied for new brp through UKVCAS but haven't heard from them since then. I tried contacting them but after few forwarding it ended up on the note that they have a large number of applications at the moment, which is taking longer time then expected. I have applied through standard application in UKVI. My brp is valid till may 2023. I am concern about my immigration check while returning to UK which needs my physical brp.

I looked online that there is a thing called 'brp replacement visa' which lets me travel back to UK only once. But to apply for it I need to go to another country first, I cannot do it from inside UK, and there is no guarantee that I will receive my brp replacement visa in such a short time interval.
I don't have any advisor in UK to support and advise me on this tough time. I seek out for immediate help and advice from people who have already been through similar situations.

Regards
Parag