I'm fairly sure that the Hyundai i10 and i20 have conventional (and therefore more reliable) automatic transmissions. Her budget should get her a nearly new one.

Used Yaris HSD. CVT which she is used to. Bulletproof reliability. Mine was quite possibly the best car I have ever owned.

Three choices in that budget

Honda Jazz Mk1 1.4 CVT, post 2005 facelift

Honda Jazz Mk1 1.4 CVT, post 2005 facelift

Honda Jazz Mk1 1.4CVT, post 2005 facelift.

look for a late 08-plate in top spec EX trim

No I dont own one, but I have two relatives with them owned from new on 07-plates. The sun rises and sets with their cars - utterly reliable. They change the ATF annually in the gearboxes. Both cars do 95% short journeys.

The Nissan Note 1.6 Auto (up to 2012/13) with traditional auto box with overdrive is a great car.

Suprisingly economical , very reliable with a nice high up driving position (great visibility)

It's also very easy for people to get in and out of.

Edited by Big John on 26/02/2016 at 21:45

I'm sure one of the things that would have drawn your Mum to the unreliable over-rated A-class was the elevated driving position. In which case the Suzuki SX4 Auto could fit the bill. They are nice to drive, very reliable and cheap. Engine noise can be excessive at speed but if she's just pottering around town this shouldn't be an issue. £5K will buy a nice 5 year old example.

Don't bother look at electric cars, as in your mum's case:

1. They are expensive for those doing low mileages (high purchase cost);
2. Charging stations are VERY few and far between and don't take 5 minutes, so all those nice frozen peas bought at the local supermarket will have been well on the way to being defrosted by the time it was done. Similarly being on low charge when out at a friends might end up in her being stranded on a busy main road on the way home if it runs out of power (most have a very short range which might last say 50-80 miles) - its not always easy to judge how far you've got left if the weather is changeable and she needs to use the A/C or heater which consume a LOT of power in electric cars (no heat given off by the IC engine to help warm the airflow);
3. They are a new technology and (as my elderly parents will attest to) won't likely go down well as its all to much wizz-bang inside. They just want something easy to use that's not complex and is reliable.

As such (as others have said), go with the small, Japanese (/Korean) and petrol - Jazz/Yaris/Mazda 2/i10 or i20, etc with the LEAST amount of electronic gadgets as is necessary. The only thing to worry about is whether to have tea or coffee when she gets it serviced.