Paying for Virgin Media mistake

My 87 year old mother has been a cable TV customer for years and perhaps two years ago, her provider changed from NTL to Virgin Media. This was a 'seamless' transition apparently, mum mother didn't need to do anything, as Virgin Media assured their customers that their service would not be interupted - just improved.
I've just contacted Virgin Media on my mother's behalf to cancel her broadband service as it's no longer required. When they checked the details of my mother's account, they discovered that for some time they had been giving my mother a staff discount by mistake, and that they'd been undercharging her by something like £30 a month. They are now demanding the arrears.

Do they have the right to make my mother pay for their mistake?

Thanks Chutzpah,
I had already contacted Consumer Direct via email, and received their reply this morning. Their suggestion is to cancel my mother's contract with Virgin Media, stating the reasons why they should waive the arrears as it is their mistake and my mother is on fixed income - and give them 14 days to respond.
This would leave my mother without a phone line - which is vital at her age and level of disability. It would also leave her with no entertainment at all, as she cannot receive terrestial TV Broadcasts, and cannot afford - nor would she want - Sky installation.
It would appear from Consumer Direct's response, that there is no legal cause for Virgin Media to accept the cost of their own error, and that the only hope my mother has is an appeal to Virgin Media for compassion. I had hoped that in these days of accountability, the 'rules' would state that the Virgin Media employee who made the error would have to pay the debt. Not an elderly customer who had no reason the question the charges Virgin Media requested and paid her bill in good faith every month.

Bit of a sad state of affairs i would say.