The NHS may be stretched, but it provides an awesome selection of free healthcare for insulin dependent diabetics.
You'll need to register with a GP, (and possibly pay an immigration health surcharge when you enter the country, depending on your visa.)
Have a close read of this link here.
https://www.nhs.uk/using-the-nhs/nh...ngland/how-to-access-nhs-services-in-england/
Visiting a GP is free in England, and you'll probably qualify for free prescriptions as well, due to being a diabetic. If not, then you should be able to get a prescription prepayment certificate for 30GBP for 3 months. GPs give out scripts for insulin, pens, needles, lancets and test strips. It may be more tricky if you need to access pump supplies or continuous glucose monitors. It's possible that your GP won't want to prescribe as many strips as you need, there's a wide variety available to buy without prescription but I'd recommend asking your GP first.
Have a look at this link as well.
https://assets.nhs.uk/prod/documents/Using-the-NHS-Information-for-visitors-from-abroad.pdf
I haven't lived in the UK for a while, so someone else may come along soon to give you better advice if I've got the above wrong.
As long as you're covered by the NHS, then I don't think that private health insurance will help. (They tend not to cover pre-existing conditions).
Hope the above helps. (And apologies if I'm out of date on the advice).