How can I get prescribed sleeping pills?

Yes, you said the same nonsense in one of the previous threads too.
Constant drip drip of info as people recognise you.
In the meantime you omit info so people tell you what you want to hear.

Reasonably healthy apart from the alcohol, and I would usually have a salad for dinner at least 3 times a week and usually eat more veg. My diet is clearly healthier than an average person’s and my doctor agrees on that

“Hi doctor I take 50mg of codeine a day and have about 8 units of alcohol a day, please could you prescribe me some benzos”

Most people would only include information directly related to the topic in a forum post and wouldn’t tell their whole life story

Common side effects of codeine:
Constipation
Feeling or being sick (nausea or vomiting)
Feeling sleepy
Confusion (unable to concentrate or think clearly, muddled thoughts)
Feeling dizzy and vertigo
Dry mouth
Headaches
https://www.nhs.uk/medicines/codeine/side-effects-of-codeine/
And as you said yourself: "apart from the alcohol"... "about 8 units of alcohol a day" (a bottle of wine has 9 to 10 units).
When are you going to stop drinking alcohol (with you telling your doctor that you will be doing so)? So that your self image of you being "reasonably healthy" in what you eat and drink can take a giant leap towards being anywhere near close to the reality?
With you then monitoring the effects that this single change has to your stomach pains, headaches and sleep.
Edit: and as for mixing codeine with alcohol:
https://www.ukat.co.uk/help-guides/how-to-recognise-the-dangers-of-mixing-codeine-and-alcohol/
"Long term effects of mixing codeine and alcohol
Continued misuse of Codeine and alcohol can result in long-term health consequences, such as liver damage, gastrointestinal issues and addiction. Chronic use may lead to tolerance, requiring higher doses for the same effects, increasing the risk of a fatal overdose."

“My addictions to alcohol and over the counter painkillers, (for which I regularly travel to multiple pharmacies so that I can exceed prescription limits), are not relevant to this thread in which I ask for advice in obtaining sleeping pills, an addictive and controlled category of drugs”.
I appreciate that you’ve said that you’ll only post whilst drunk or bored, but do you ever read this stuff back to yourself?

“Hi doctor I take 50mg of codeine a day and have about 8 units of alcohol a day, please could you prescribe me some benzos”

I’ve had sleep problems since I was a kid so pretty sure anything else which started much more recently and has had no effect on it isn’t relevant here

Yes, and they might be minded to look at why it is that you're drawn to misuse all those substances and what underlying issues may be the cause for that and treat those, negating the need for you to be prescribed sleeping pills, pain killers, and to abuse alcohol...

How long have you been having the stomach pains?
How long have you been having the headaches?
How long have you been consuming codeine and alcohol?
Do you think you'd sleep better if you weren't getting the stomach pains nor headaches?

My sleep problems are entirely unconnected to that though and I don’t want to say anything that would increase my changes of being further dismissed/not believed by my doctor or being labelled a drug seeker

And again, you know this is unconnected due to your medical degree...?

I know it’s unconnected because the sleep problems and pain have been going on for years longer and I’ve been drinking less all summer until very recently, and had an entire month without alcohol, which didn’t make any difference

That doesn't mean that the pain isn't connected to the sleeping and the drinking could be a way of coping with those issues. Realistically you aren't medically trained (nor am I or anyone else realistically going to comment on this thread) which is why you should tell your doctor so they can actually assess the information and make the determination for themself whether there is a connection or not and address it accordingly.

Which prescription strength sleeping pills would you be looking for your doctor to prescribe for you?

Lorazepam or diazepam

these are not sleeping pills

I’ve tried melatonin and it makes me ill

how does that make diazepam the answer?