How long can most people go without binging?

It's not very normal. The main difference is not being able to resist I think. To be fair most people eat or drink more than they intended occasionally, but it's not in a problematic way and they could have chosen to consume less.
Honestly it sounds like you're over-restricting yourself on your normal days. Assuming you're at least like 14, if you're 6 stone 10, it's not healthy for you to lose weight, and 1200-1400 calories is not enough to subsist on. A normal, healthy amount is 2000 for a woman or 2500 for a man, or more if you're a highly active person.
You're probably feeling urges to consume more on your binge days because you're not getting enough to eat generally and your body is forcing you to compensate for that.

I'm 21 but I'm 5'0 so that is a healthy weight for my height

Your BMI puts you in the underweight category.
To answer your question, I never binge eat now that I have recovered from my ED. I overindulge sometimes, but there is no feeling of being out of control like there was with binging. I have never binge drank alcohol.

According to the BMI calculator I use, my BMI is 18.5 which is exactly on the border of healthy weight

If you’re exactly on the border of being underweight and experiencing irresistible binge cravings, what does that tell you?

Because of my body type and the way my body stores fat I look heavier than I am so a BMI of 18.5 for me is the same as a BMI of maybe 22 for anyone else

that's what everyone with an eating disorder thinks

Most people don't really binge as such, slight excess isn't the same thing, and this is one of those deals where if you're opinion is already "I know most responses will say that normal people don't binge at all on either food or alcohol but they do" - then it's pointless, you're already trying to distort other peoples experiences to talk down your own, it's not in any way subtle.
"BMI of 18.5 for me is the same as a BMI of maybe 22 for anyone else" - likewise, no, you don't get your own set of rules.

Most doctors/mental health professionals won't even entertain the idea of someone struggling with disorder eating unless they're (usually pretty severely) underweight though

I've asked people on fitness/weight loss forums to guess my weight/BMI or say whether they think I'm skinny, average or chubby and they nearly always guess that I'm at least a stone heavier than I am and say that I'm average rather than skinny

Not true. Most people with bulimia are not underweight and are very much still acknowledged as having an ED. Sounds to me like you are just looking for excuses to not deal with your issues.

I'm not saying your lying.. but this is internet randos, many of whom will not want to offend by given any answer other than 'averageish/good!' and they're going off a photo or two that you have chosen rather than unbiased measurements. Their opinions aren't worth a lot is what I'm saying tbh.

The unbiased measurements all say I'm healthy though. My BMI is 18.5, body fat is around 20% (I'm female), and waist-hip ratio is also in the healthy/ideal range

Just to be clear, when you say your 18.5 is on the border of healthy weight, that also means it's on the exact same border for unhealthy weight, correct?

18.4 is underweight, 18.5 is the start of the healthy weight range

and yours is 18.36

I'm a healthy weight and eat 3 meals every day, no doctor is going to say I have an eating disorder just because these meals are relatively small and I sometimes over indulge/binge