How to deal with disordered eating without speaking to someone

I’m not significantly underweight (5lbs under) and not planning to lose any more so my body definitely isn’t “frail” or under any significant strain

Well you tell me, why do your hangovers last for days? It's not normal.
I mean, c'mon... You keep binging on junk and booze, fuelling yourself with crap and it takes you days to process the alcohol and you've previous lost your periods... and you're going to sit and tell me your body isn't straining or frail?

I’m just not a very likeable person I guess. I’ve never had close friends. I’m quite quiet/introverted and people don’t warm to me easily.

I don’t have an eating disorder as in the diagnosable mental disorder, I just struggle with disordered eating as in some of the behaviours but not to the point of it being a disorder. And I am technically underweight (bmi 17.6) but because of my build I don’t look it. My thighs still touch most of the way up and people would probably look at me and guess I’m about 8.5 stone.

I don’t want to wake up every morning in a disgusting fat body and even when I was maintaining a weight at the lower end of healthy, my body was disgusting. I have an unfortunate build which doctors wouldn’t take into account and it’s not worth a lifetime in a fat body I hate just to reach what a chart classes as healthy

There are several points I want to address here, but they all ultimately come down to this - you are not in a position to judge yourself.
I haven't ever met you, but from what you have written online you strike me as an eloquent, polite, respectful and fairly mature individual.
Whereas you are describing yourself very negatively, and I am unsure why.
Second thing is the BMI stuff. My current BMI is 19.1, which has increased slightly from being just in the underweight category. It is obviously more sensible to be in the healthy range - any responsible adult is going to tell you that. Does that mean all 20 year olds are sensible? No, they aren't.
I'm not a doctor, I'm not going to prescribe you with anything and you have been recommended some really great resources from Beat, and I recommend you use them. The only advice I have is to develop a routine. Humans like routines, our brains crave them; this is not just for your eating pattern but your overall wellbeing. Try to eat at consistently similar times, with consistently similar things. It may be boring, but even if you are eating exactly the same food every day - it's a starting point. From what you're describing so far you're swinging between extremes. You need to establish what normality looks like for you. Or "ordered" eating, I suppose.
Final thing to talk about is perceptions. There is a reason that doctors won't take into account "an unfortunate build", and that's because medically that doesn't matter. It obviously matters to you, you are 20 and you care about how you look. Makes sense. Also you are right - everyone's bodies work differently, we are all different shapes and sizes and what works for one person may not for another. Don't distrust medical advice from a qualified professional though. What does concern me is this phrase: "people would probably look at me and guess I’m about 8.5 stone". You do know that people don't do this right? It's not normal to look at someone else and start getting their weight That's not a normal human behaviour. Unless I'm picking you up and lifting you off the ground I couldn't care less how many kgs you have. So my final message is if you want to care about how you look, fine, if you want to care about your own body and want to be your best self - I can understand that. But don't you dare change yourself based on what you imagine other people might judge you for. Anyone, anyone, who makes judgements like that is not worth being in your life. Parent, friend, lover, stranger, anyone making surface judgements about you based on your appearance can jog on. Please, cut those people out.

I’m not trying to change myself for anyone else, I’m going for a look I prefer. Unfortunately, with my build, achieving a “skinny but healthy” look would require me to have a much lower bmi than most people

What you are describing has similarities with body dysmorphia, yet again id really encourage seeking support

I knew that’s what most of the replies would say but seeking support isn’t something I’m considering at the minute

I’m not trying to change myself for anyone else, I’m going for a look I prefer. Unfortunately, with my build, achieving a “skinny but healthy” look would require me to have a much lower bmi than most people

Who are you trying to convince? Me, or yourself?
To quote your own words back at you: "people would probably look at me and guess I’m about 8.5 stone." You are worried about how other people see you, that much is very plain. Arguing against that isn't going to wash.
It doesn't matter what your build is - I gave you some advice about how to live sensibly with food and weight. Your build doesn't change my advice.
You seem as though you are trying to justify a low BMI, I don't think I've made any comment about your BMI - which I'm guessing means you are actually just trying to convince yourself.

I think you need it though. By posting this alone you are trying to reach out for help and support. But TSR can’t be with you in your everyday life

I’m not trying to change myself for anyone else, I’m going for a look I prefer. Unfortunately, with my build, achieving a “skinny but healthy” look would require me to have a much lower bmi than most people

I get migraines and naturally get a headache really easily so I’ve always had bad hangovers. When I’m not binging, I eat healthily and eat a lot of fruit/veg. I’m not going to pretend I’m in peak health but I wouldn’t say I’m much more unhealthy than the average person

I was expecting at least a few people who had been through something similar to suggest self help strategies but my current plan is just to maintain the weight I’m at until I no longer feel the need to restrict/preoccupation with food/weight

You 'naturally' get headaches really easily? This isn't doing much to convince me of your body not straining

Saying that people would guess I’m around 8.5 stone was more to give an example of how my build makes me look much heavier than I am. I’m not worried about people finding me unattractive (if anything I got more positive attention for my appearance when I was a stone heavier)

Maybe try to meal prep and add in one/a few small healthy snacks a day to get your eating patterns more regular

I just eat my maintenance calories currently, adding anything in would make me gain weight

If you are not willing to change what and how much you eat, how are you hoping to change your disordered eating?

I want to stop binging and stop things like constantly thinking about food/calories and dreading spending time with my family/holidays like Easter because I won’t be able to avoid eating