You need to be seriously unwell to get them, or at risk. You are neither. You're only 12 stone. If there are people with a BMI under 40 and they are getting the jab, then they've paid for it online and lied about their BMI. A surgery will go through rigorous examinations, but online is just a tick-box and you can lie. Most will ask for a picture of your entire body from several angles to prevent you from lying. Otherwise, if you're willing to pay between £160 to £400 (lower dose is always the cheapest), willing to lie and risk your health.. anyway.
I have friends who were 12st when they went for a gastric sleeve, friends who are now confused as to why they are so underweight, and still losing weight...the weight loss doesn't just stop when you want it to. It does slow down, but having jabs and operations when you're only 12st in weight, is very risky. I was once 30st, I'm now down to 16st 7. It's hard work! I had a sleeve, last year. I've also had jabs. I've used mounjaro because my weightless slowed down - It's a massive headache game.
I've realised that counselling, using a nutrition app, exercise (not by much!) All go hand-in-hand with losing weight. However, obsessing over it is now healthy. It doesn't need to be difficult and depressing, so please don't live your life by the scales...you need to eventually draw a line and accept happiness somewhere along the road, or you'll forever keep walking this path and get nowhere with it.
There are online NHS weight groups you can be referred to, they provide counselling, and a psychologist Dietician. Might be worth asking your GP about that if you're struggling. I found the groups pretty good. You can also get gym referrals for a 16 week period, for free, from your GP if they do that where you are.