There is a light that shows when the battery is NOT being charged. A bulb/LED is there as an indicator, to show you something. The battery is charged by the alternator in a car. I would go to a different garage and would be asking for the £150 back or going through the small claims court and trading standards. The garage I use does not charge if the car is not repaired. I would have refused to pay if I had a car returned with the same fault and unrelated parts were replaced.
Why would you be charged £70 for a diagnostics check? Is that from the same garage that couldn't diagnose or repair your car? Do it yourself.
Hold the brake and accelerator right to the floor (if a manual gearbox). Turn the key to position 2 but do not start the car. The mileage display will change to "ECN" and a series of numbers will show where the mileage is. Make a note of each set of numbers as it cycles through. There is a huge list on this forum that will give you an idea of where to start looking to solve the problem.
Post a message asking for help with the error codes. If your alternator isn't working your steering goes very heavy and the battery drains very quickly. That's when you will see the red light. A power drain from a glowplug is at least "original" !