It is possible to buy home tests which can give you your HbA1c in a matter of minutes. Of course you have to buy them.
Have a google for the brand name A1CNow or A1c NOW and you will find them. There is quite a lot of debate on whether they are accurate enough, since they aren't NHS lab tests. I figure they are probably accurate enough to give a ballpark figure.
Otherwise you are stuck with the frequency of HbA1c tests that you can persuade your nurse to give you.
If you want to know the actual accurate results of ALL your medical tests, you need to ask. Your nurse will be reading the numbers off the screen, and then dumbing it down for you, the patient, into plain English. Don't know about you
but I ain't dumb, so I want the actual numbers please. Don't let them fob you off with platitudes. It is YOUR health. You live with it every day, and the numbers are IMPORTANT.
(had a hilarious situation with my doc recently, where he took my blood pressure. When he had finished, he turned to his computer and started tapping the keyboard. So I asked what the result was. He ignored me. So I asked again. He ignored me. So I asked again (we could have gone on all day, and I think he realised that..). So he told me. The appointment went downhill from that point! haha!)
You can get the results of any of your tests by asking the nurse or doc at the time you see them, or ringing the receptionist and asking. Sometimes the receptionist will refuse to give the numbers out, but just push a bit, and they may offer to get the nurse or doc to call you. Keep asking til you get somewhere. You can also ask for a printout, from nurse or receptionist. Alternatively, you can ask for online access to your test results (surgeries are required to offer this service in the UK, since April 2016). The receptionist can tell you what the set up process is.
Don't worry about understanding the numbers they tell you. You can look them up online, or ask here, and we can point you in the direction of how to understand them. That chart I posted higher up the thread will give you a good indication. Green is good. Amber less so. Red needs action NOW.