hamster58.
Rather looking at the monthly direct debit amount, have you looked at the monthly/quarterly bills to see how many kw/hrs of electricity are actually being used, and how this differs throughout the year?
You would expect to see that your mum is using far, far less electricity in the summer months, when those electric radiators should rarely be on.
If that's not the case, there is something strange going on that needs looking into.
In fact, if you want to confirm that the radiators are the problem, might it be possible for you to take actual meter readings both morning and evening on a day when the radiators are in use, then do the same the next day (perhaps taking her out for the whole day so she needn't be too cold?) so you can get a rough idea of how much they use each day?
I realise that this might not be practical unless you live close to your mum, and would also have been most 'telling' if done in the cold winter months when the radiators are using most energy, but even done now, it might shed more light on the problem.