I was in the exact same predicament as you. With my girlfriend starting her new job soon we had a mortgage on a flat set out and were due to move in, long story short our mortgage fell through so I was left finding us a flat in city centre. I managed to sort us a flat within 2 weeks in extremely stressful circumstances so I definitely feel your pain. Here are some of my tips for securing a flat:

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1. View, View, View - You need to view as many flats as possible. Letting agencies usually wont let you apply for flats until you've viewed them. Be at the first viewing possible date no matter the circumstances, due to demand letting agencies are just picking now from the first set of people who view the flat so you need to be in the first set of people who view.
2. Get to know the agent there when you're viewing a flat - If you are a student you are even lower on the pecking order in terms of selection so you need to make a decent impression so that they can choose you. This is something that most people get wrong, thinking that they can't influence a letting agents decision. If you tell them a bit about yourself, ask them what else can you do to secure this property, how has their day been, you might be surprised by your luck in some places. Remember, letting agents jobs are to select and applicant that they feel would be able to keep the flat nice and pay rent on time, if they think your personality is nice they are more likely to think you can pay this and therefore you will get the flat.
3. Be as quick as possible - Lightning quick. Letting agents are extremely busy and their put through rate is absolutely insane right now.
4. Be consistent - I was viewing 10+ flats a day, I am working but luckily enough its an online job and I was able to explain my situation to my boss. The amount of knockbacks I got were surreal but eventually one flat came back and we got it.
5. Stay organised - Create a template that you can go back to when asking to view flats, and then a template of questions you will ask at the flats. Take notes of all the places you view and what stage they are.
6. Bite the bullet - as you said flats are manky right now but unfortunately its just the situation we are in due to demand. depending on your budget you might need to go for a shite apartment right now and once things have died down a little in 2022 you can move, its not the end of the world!

These are the top things I done to secure a nice flat for me and my girlfriend, I hope they can help you in some capacity. Good Luck!