If you accept that these were genuine accounting errors then you are liable for this cost. However they cannot simply demand and expect to enforce payment over an unreasonable period.
There is no reason why your insurance company should not pay this if it was in respect of the treatment which was covered by insurance.
If it is not covered by insurance for some reason and you pay it, I will tell you how to deal with that. If the insurance company in your opinion are liable for this, and they simply will not pay, then make a complaint to the fails, make a further complaint to the Financial Ombudsman Service.
Ultimately you are liable for this, paid £50 per month and ignore the protestations. It is likely, even if they issued court proceedings straightaway, that this would not be in court for probably 10 or 12 months by which stage you would have already paid back half of the money and the court are then unlikely to make any order than to pay the £50 per month back continuing until the debt is extinguished.
They did take it to court based upon the circumstances here it is possible that the court would say they are being completely unreasonable and award costs against the doctor even costs are not routinely awarded in the Small Claims Court.
Just keep paying £50.
Can I clarify anything for you?
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