Hi m_cooper and welcome to the forum.
If your test showing an average of 9 was an HBA1C then the figure is a percentage, not your blood sugar level. An HBA1C of 9% equates to an average BS of around 12mmol, which is very high. As an HBA1C measures your BS over the previous 3 months, it is quite likley that you have had pretty high blood sugars for quite some time before diagnosis without realising it. What this means is that it is more likely that the burning sensation you are experiencing is the early signs of neuropathy (nerve damage). However, early stage neuropathy is usually reversible by reducing your blood sugar levels. So it is important that you concentrate your efforts on this as soon as possible.
Looking at your diet it does seem a bit heavy on carbohydrate, which of course is what creates blood sugar. If you are ok with eggs (i know some people can't stand them) then substitute your breakfast cereal for a couple of eggs (boiled, scrambled, poached, fried, in an omelette) perhaps with some mushrooms and tomatoes. For lunch either drop the beans, or at least ensure they are sugar-free (half the carbs of standard baked beans), and for toast use Burgen, WeightWatchers or Nimble bread (half the carbs of normal bread). If your evening meals includes potatoes as one of the veg, then drop them and have a different veg instead. Try this for a week and you should see a big difference in your BS levels.
That will help reverse the nerve damage and get rid of the burning feet, unless of course you want to rent yourself out as a patent hot water bottle!
Oh, and get yourself a blood test monitor. Trying to control your blood sugars without one is like driving a car wearing a blindfold! Ask the nurse at your surgery if she has one she could give you. If not then they are available at any chemists and are not particularly expensive (anything from £6 to £20 depending on the make and model). It is the test strips that they need that are costly and you may have to fund them yourself as surgeries are reluctant to prescribe them on cost grounds. One idea is to check with your chemist which model needs the cheapest test strips.