@Hughes87 If you are genuinely dropping that low (as oppose to a compression low where Libre reports a false low when you lie on the sensor) before you get up in the morning as well as dropping low after your meal and after you go to bed, then it sounds like your basal insulin is also too much. Which basal do you use and when do you take it?
The key thing about diabetes management is that nothing is set in stone, so you might be injecting the basal dose or right amount of bolus for the carbs you are eating that worked last week, but these things change, both up and down in response to a large number of factors. Alcohol is one and exercise is another which can cause these sort of drops and will have an affect for much longer than the time you participate in them. I always have to reduce my evening basal insulin dose after exercise otherwise I will hypo every time. I seem to be much less responsive to alcohol and hardly see any effect but others have to eat unbolused carbs with their alcohol to prevent hypos.
If you are on a very long acting basal insulin like Tresiba or Toujeo, then you are limited in how much you can adjust them for exercise and alcohol and you probably need to reduce your evening bolus more and perhaps push your levels up high before you go to bed to counteract the drop in BG through the night. If you are on a shorter and more flexible basal insulin like Levemir or Lantus, you can reduce the dose accordingly once you figure out what the factor is which is dropping your levels and therefore when you are likely to experience these drops.
I have Levemir as my basal and whilst my daytime (morning) dose is fairly stable, my evening dose is the one that I need to adjust to compensate for any exercise I have done during the day. You gradually just get a feel for what works for you but it tends to be quite intuitive rather than calculated.....it is for me anyway. My evening dose can range anywhere from 0 to 5 units. My morning dose is mostly 22units but can go up to 24 or down to 20. If I have adjusted my evening dose, it is generally not a good idea to also adjust my morning dose as that is usually too much in one day.
It is also important to understand that exercise is not necessarily formal exercise like running or going to the gym but any prolonged physical work like gardening or washing the car etc.