Hello. Sorry to hear about your mum. You must be very anxious.
Your GP is right to say that a having an anaesthetic carries some risk.
How much or how little depends on your own state of health and the type of operation and anaesthetic that you are going to have - this may all be very different indeed to your mother's situation.
Without knowing the details it is impossible to be specific.
The very best people to answer your question are your Anaesthetist and your Surgeon. You should get to see them before the operation.
You may also be asked by the hospital (though not necessarily) to attend a pre-operative assessment clinic. This may also be a good opportunity to ask the question about risk.
For many people this risk can be considered "small". They may then decide that that it is OK to go ahead because the benefits they stand to gain from the operation are worth the risk. There are, after all, risks involved with many things we do - like driving in a car, flying in a plane, going swimming.
The best person to decide this is yourself.
In the meantime you may like to check out the website of the Royal College of Anaesthetists. This is the professional body responsible for anaesthesia in the United Kingdom.
If you go to the section under the heading "For Patients" you will find lots of very clearly written documents. These answer your question, and others, in more detail and with more authority than I have done here.
The most general one is "You and Your Anaesthetic":
http://www.rcoa.ac.uk/docs/yaya.pdf
This page talks about risk in more detail:
http://www.rcoa.ac.uk/index.asp?PageID=816