First point, is your BMI over 30 or over 27 with a weight related health condition, or over 27 whilst being one of a list of specific ethnicities?
If so, to get started, you apply online for a private prescription from one of the online pharmacies that supply the medication.
This is a price comparison site for suppliers:
https://monj.co.uk/discount-mounjaro-price-list/
Check that the pharmacy you use is registered with the GPhC, although all the ones on that list will be.
You typically fill out a consultation form giving your medical history, height, weight and so on. Then you are offered a choice of medication, usually Mounjaro or Wegovy. You choose which one you want, and apply. You then pay for the first prescription, and your application is then reviewed and hopefully approved. Most pharmacies will ask for current photos of your figure and/or ID to be uploaded as part of the review process. It's then sent out to you via RM or a courier or some places you can collect from a pharmacy (Asda, Boots do, there are probably others). The injection pen needs to be kept in the fridge before you start using it. There are 4 doses in each pen, so a pen lasts for a month.
Mounjaro, you start with a dose of 2.5mg injected weekly. After 4 weeks on that you can move up to 5mg or ask to stay on 2.5mg if you feel it's working well for you. You can move up to a higher dose after at least 4 weeks on the previous dose.
Some suppliers do a subscription model where the next prescription and higher dose is sent out automatically unless you actively change the order. Most will wait for you to manually re-order your next prescription. Some suppliers offer coaching and additional support as well as the medication. Your choice as to which model you prefer.