Can the bank make mistake?

[romvig]

In April 2010 I received £2100 pounds from my mother via bank transfer. Then several days later I received the same sum of money from the bank once more. I suspected that my mother sent it second time round by mistake, but nothing prevented me from spending all this money. Some time later my mother had a call from the bank and was told that they made a mistake and sent £2100 pounds to me twice. Can her bank take money from my accounts without my consent?
Thanks in advance