GP letter needed urgently

I am a uni student needing to defer my exams, but uni want a letter with only 14 days to do it.

My close family friend passed away last week. I have had an exam and more exams in a few days. I've been a mess. Not sleeping, not eating.I can't concentrate. I just cry all the time. I took one of the exams and realised how messed up I was. I could hardly read the screen, eyes blurry. Reread questions over and over. I was dressed back to front, brought the wrong bag. Kept failing to sign in because I was misspelling my password. My friends told me to sit it out, but I was terrified of failing to turn up and not even being offered a referral.

I have accepted i need to file for exceptional circumstances, but the process looks so confusing and if I'm honest impossible.

I have no access to the death certificate and the funeral has not yet happened. So no order of service either.

I informed the uni of the situation and they said get a GP letter to provide evidence of the impact on my health/performance.

However, I get 14 days after the exam is over to file and supply evidence.

My last exam was Friday 2nd May, and my next is Tuesday 6th May. It's been a bank holiday weekend. My GP wasn't open and won't be until Tuesday. But from all advice I've been given it will take a minimum of 14 days for the letter. So will miss the deadline.

From experience is it likley a GP would be able to provide a letter faster if there is a deadline like this?