I had this problem with my late husband who had a rare form of dementia affecting vision and co-ordination. Problem is that they have no insight into their impairments, so it just appears that everyone else is being unreasonable. On account of the difficulties we had with him, I'm currently involved in a national group making recommendations regarding dementia and driving. The group comprises medical consultants, GPs, DVLA, Alzheimer's Society, the Mobility Centres and others. It should be publishing recommendations by the summer. Jackypat, I realise that you haven't mentioned dementia, but early dementia is often underlying the problems mentioned. For information, anyone who has a diagnosis of dementia MUST, by Law, inform the DVLA and their insurance company.
However, if there is no diagnosis, as in your mum's case, you can write to the DVLA about her, giving your reasons fairly concisely. You must give your name, but they will not reveal their source. Their medical section will most likely send your mum a letter asking her to attend a local Mobility Centre where she will have a driving test and perceptual assessment, following which, they might recommend she cease driving, or offer her a driving licence for a restricted period before re-testing. Many people voluntarily cease driving rather than take the test. You can also talk to her GP. They are not all sympathetic, but many are. If they get a request for medical information from the DVLA, it's best if they are fore-warned that the family think there's a problem.
You can use the economic argument with your mum and dad: you can buy a lot of taxi rides for the price of fuel + insurance + depreciation & you can get a contract with a local taxi firm for very good terms. You are doing the right thing. Good luck!