I think it's probable that the doctor's view of statins was and is that the cardio-protective benefits outweigh the risk of diabetes developing. Not everyone on statins develops diabetes. I'm not saying I agree with this view, but it's basically what the doctors' guidelines say.
I'd recommend taking a cautious approach when discussing all this with your doctor, as she might see our ideas as controversial (at best). Our collected wisdom and the research we are aware of is placed up against their training, research, and guidelines. Doctors have a tendency to rely on the latter and shut out other ideas, which I think is understandable. It's their head on the block if something goes wrong.
Ultimately though, many of us have demonstrated to them with cold hard facts like lower blood glucose, cholesterol, BP and weight, and they then cannot ignore those facts. I think the smart approach is to mainly keep these ideas up your sleeve until you can show them the results of your hard work later. Some people start off by telling their doctor the wonderful things they have been learning here and are then shot down and treated like a naughty schoolchild. Your doctor sounds more professional than that but hey, I'm cautious I guess.
As you noted above, you have a few cardiovascular risk factors, so statins might be appropriate for you. And, who knows, you might have developed prediabetes anyway. A lot of this is speculation. To keep things simple, reducing carbs and weight should reduce blood sugar and cholesterol and cardiac risks... to a point where you may not need statins, or medication for diabetes. Probably something to put on the back burner for now, unless you are getting bad side effects from the statins, like muscle problems, for example.
I ran your weight and height through a BMI converter and the result was 31.5. 20-25 is "normal" and 25-30 is overweight. My own BMI was once 44 - yikes. Research shows that people start to see benefits after as little as 5-10% weight loss, which I think is about 1 and a half stone for you. I predict you will achieve this is in no time at all
Once you've done that, you just keep on going until you reach your target. It's easier than you think.
You mentioned you've been on borderline BP meds? The recommended upper BP limit for people without diabetes or cardio-vascular disease is 140/85 and for those with diabetes or CVD it is 130/80. I would suggest with prediabetes and raised cholesterol and your family history the lower target is a good one to aim for. I'm on a low dose BP med and it keeps my BP well under control and it also protects my kidneys from damage. There is something about high BP, diabetes and high cholesterol that makes these 3 things go together and make each other worse. So we have to tackle them on all 3 fronts.
Managing slightly high BP is about the easiest part of all this, because the first-line drugs are usually well tolerated, and diet and weight loss aren't as important as they are with diabetes and high cholesterol.