As others have said reciprocal UK-Oz arrangement is ideal. There is Pharmaceutical Benefits Scheme(PBS) here in Oz is tied in with Medicare, our version of your NHS. (although there are some distinct differences as described below.) PBS reduces costs considerably for commonly prescribed medications e.g. Novorapid i use for my insulin pump - i have pen cartridges prescribed - for 5 packets of 5 cartridges at 300 units per cartridge is AUD 36 ( full price without PBS = AUD 410.) Insulin pumps are a little in flux. Medtronic and Roche are currently supplying but Animas is leaving the pump market and being replaced gradually by Tandem as Animas pump warranties run out over next 2 years or so. There are the only pump companies approved by Govt to sell and supply pumps, parts and servicing of pumps here. NDSS, National Diabete Supply Scheme is also available under reciprocal arrangment and provides testing strips, syringes and cartridge/reservoirs and needle insert pump supplies at reduced cost. Diabetics under age 21 receive rebates for CGM supplies but not others. So a box of 100 glucose testing strips cost me AUD 17, the same for a box of ten reservoirs/cartridges and same again for 10 needle inserts. Private health insurance obtained in Australia does not cover anyone with 'pre-existing conditions' like your diabetes for the first year on that insurance. Some tables of insurance you can apply for will help (after the first year) to cover some pharmacy costs over about AUD 60. Private health insurance once you qualify regarding your diabetes does offer some rebates on new pumps. The amount varies from company to company. The Govt have a Medicare system for pump supply but the waiting list is long and number of new pumps supplied is limited. See what medical insurance you might be able to obtain in UK for Oz. In Oz we pay for GP visits and then are reimbursed some or all of the cost through Medicare. It depends on what the GP charges. But a Medicare rebate of about AUD 35 applies for a standard 20 to 35 minute GP consultation. You may be charged that fee but often more e.g. AUD 60. We also may pay over the Medicare rate for pathology and imaging although some do charge Medicare rate ( called bulk-billing). As per most public health systems there are hospital clinics for diabetics including for eye problems etc. Specialists in private practice are partially covered by medicare rebates but like GPs few bulk bill. Under Medicare, GPs can arrange Diabetes Care Plans which provide rebates for a total of 5 visits to a mix of allied health professionals such as diabetes nurse educators, psychologists, dietitian, podiatrist etc.( Most accept Medicare rates of service but not all, for example a psychology consult may leave you AUD 30 to 40 out of pocket). Medicare does not cover dental fees unless you are in a disadvantaged group. I would suggest you try to get any urgent or semi-urgent dental care done in UK before you leave. Private health insurance in Oz under some tables of insurance provides limited dental rebates.
Cost of living varies from State to State and capital to capital. Sydney is most expensive then Melbourne, Brisbane. Canberra can also be expensive due to rental shortages and the cold climate through winter.. Other capitals such as Adelaide (were i live), Perth, Hobart, Northern Territory much less so. If your employer provides some rental assistance that would make your life less stressful !!
I hope the above does not put you off coming to Australia. Canberra is a cold place in winter, Hobart less so. Most other places have warmer summers and winters than the UK and all capitals except Canberra are near the sea. The lifestyle is generally laid back. Please do not hesitate to message me when you arrive bus pm or before for further advice particularly if you are going to be working in Adelaide or Canberra (where I have relatives). My experience of visiting doctors and the lab standards regarding HBA1C is that 7 or below is desirable. The criteria for going on an insulin pump is that control is impaired to the point of being above 7.5. I cannot advise you on exactly what the immigration medical standards are but the above suggests that a HBA1C of 7.3 is not too bad at all. One can of course put forward that the whole process of arranging to move to Oz is stressful and that one would expect that less then ideal control is likely. For driving in OZ the main emphasis is on control regarding absence or low incidence of hypos, particularly severe ones.