That is a big discrepancy but any haemoglobinopathies can affect the accuracy of the HbA1C. For making decisions about food choices, I would be inclined to take account of your finger prick tests. Those are pretty high readings.
Keeping a food diary with an estimate of the carbohydrate content or everything you eat and drink would help pinpoint the foods which are keeping your finger prick test levels so high.
Are you on any medication, I wonder because it would not be usual to prescribe meds with an Hba1C of only 51mmol/mol but recommend dietary changes, but likely if it was a lot higher as would be suggested by your finger prick tests or 13-20mmol/l. If that makes sense.
Do you have a means of testing for ketones as that can be a good idea if your level is in the high teens, urine test sticks can be purchased at the pharmacy.