I’m decades out of touch here

She’ll need to think about the extortionate cost of insurance for a first-time driver. It could cost as much as the car for the first year!

If you want something that’s not on its knees, you’re probably looking at £4K+ – and the standard cheap little car is the Kia Picasso or Hyundai i10. At that price, expect something ten years old and with 50K miles on the clock.

Nothing is anywhere near £500 – the pandemic screwed second hand prices and the EV rush has artificially inflated ‘fairly new’ resale values so cheap cars are rare.

Little old ladies’ cars like the Honda Jazz (any age) or Hyundai i10 (2014+) are safe bets. Very reliable; and cheap to buy, insure, and service. Lots of second-hand ones on the market so no shortage of choice. Aim to spend around £3,500. And as they were driven by little old ladies, they’re in great condition. For a bit of personality, choose a fun colour like red or yellow.

Electric cars – does she own her own house, with a driveway? I assume not, given her age. So that’s probably a non-starter.

Wants to buy a car

What’s her budget?

Actually there’s a lot to be said for £500 bangers and to find one, go to small independent garages locally – not dealerships – but an outfit that services cars and does MOTs and has a few used cars for sale. Find a car that suits, buy it and the mechanics will do the needful to keep the car going for you for yonks. Mechanics are more trustworthy than car salesmen.

I miss the rite of passage that was flicking through Auto Trader and buying a Fiesta for £300.

As has been mentioned the car is almost secondary to insurance. You’re still talking £2k a year being typical for a new driver for a “cheap to insure” honda jazz/small Kia/tiny Peugeot.

EVs even 2nd hand are too expensive still, despite them being in a glut and headlines about oversupply. A battered old last gen nissan note that will get you a pathetic 50 miles range will still go for £4k. Treat an EV as 3x the milage of an ICE vehicle and you won’t go far wrong – this rule of thumb won’t last as tech is far far better now but for the current low-end 2nd hand market of 5+ year old EVs, 50k miles might as well be 150k in terms of needing to shell out for a new powertrain soon, though of course they’re far cheaper to run and maintain if you can charge at home than a petrol.

It’s a real shame they stopped making estate cars. They were always a good bet. Usually better looked after, serviced etc. Driven by people needed that car. And made you very popular when thing needed moving.

A diesel car from 2005 or earlier should be free of much of the unreliable clutter that later models carry. We find ours copes with our driving pattern – short journeys – rather well though in her shoes I’d probably follow the advice above to get a petrol car from Japan or Korea.

£100pm insurance, check out the rate for paying up front

You can save serious money, monthly payments are a loan at ridiculous %, even putting an annual premium on a credit card is often cheaper

If you’re using a diesel for short journeys, dearieme, make sure you give it the odd long run occasionally. Short journeys with the car not getting to full working temperature can clog the particulate filter in the exhaust system

He did say

A diesel car from 2005 or earlier should be free of much of the unreliable clutter that later models carry.

and “particulate filter” was the first thing I thought of for “unreliable clutter”.

Daughter is a few years younger – still learning to drive – but from what I see and hear:
– the cautious youngsters drive a Toyota Aygo / Citroen C1 / Peugeot something (apparently they’re all the same underneath, but superficial looks are in that order), sub-1litre engine, basically a shopping trolley;
– those with better off / more indulgent parents have a Fiat 500, which looks cute and trendy but the engine is only 2 cylinders and still sub-1litre;
– I bought a Mini Cooper (BMW, not classic) to teach her in, and to my astonishment I’ve apparently got her the coolest thing in the school car park.

The Mini cost me £700, and I spent £400-odd on getting various niggles sorted, so nearly £1,200 all in; I could have paid that for a supposedly more together one, but I feel a lot more confident having paid the extra to a mechanic I trust than a seller who I don’t.

I’ve not regretted buying it; reliable, apparently easy to fix when needed, plenty of second hand parts. It’s small enough to drive easily around a city, but also solid enough for dual carriageway or rural roads. I’ve done a 6 hour journey in it, half of which was on motorways, and although it’s noticeably less comfortable for that than my BMW, it’s OK, a lot better than a Micra. And although it’s only 4 cylinders and front-wheel drive (so not a proper car), it’s surprisingly good fun to drive.

Insurance wise, currently it’s only learner insurance, so relatively cheap, but it was actually a couple of quid less than a Citroen C1. And although I’m a bit nervous about what the insurance will cost once she passes, from a little play around the comparison sites before I bought it, it was only about twenty quid a year more than the C1, and you get a hell of a lot more fun for that.

The only downside is the road tax, which is over £300 a year, and fuel economy isn’t great, due to it being a fairly old-fashioned 1.6l engine.

I’ve got the pre-2007 original BMW model with the Brazilian petrol engine, which my rather old-school mechanic says was the right one to get; the later engines look better on paper, much better fuel economy and slightly better acceleration, but that’s only achieved at the cost of a load of gubbins that are liable to go wrong. Get the latest you can find of that model, because they ironed out problems as they went along.

But your granddaughter is a few years older, so probably different considerations.

A bit late to this party.
Check what cars have low insurance groups. You can’t just judge by engine size/power. A Citroen C1 can be had in insurance group 1, but the Peugeot 107 and Toyota Aygo which are identical can’t.

My first car was a 999cc Fiat Panda, bought because it was the only combination of group 1 insurance and being able to fit in it. Even back in 2002 the insurance cost more than the car. But after a year, with a year’s NCB and a lower risk profile, I could then afford to insure a much nicer car. Which was good because the Panda had pretty-much had it after a year.

Having seen friends buy a more expensive low-power low-insurance car, and then get frustrated with its lack of oomph when, say, attempting to join a motorway, I’m glad I did it the way I did. She should buy something in group 1 purely to get her year’s no-claims that’s cheap enough to throw away after a year. Save the rest of the money to buy something nicer when she can afford to insure it: it’s a lot easier to find a nice car for reasonable money that isn’t in a low insurance group because you’re not competing with people buying their kid’s first car.

A VW Fox is group 1, can be had for <£1k and will be old enough to predate most of VW's woes. The base petrol Pandas from 2004 on are group 1. Rust issues, but if it's not too visible when buying the chances are it'll last a year before it becomes a liability; powertrains generally ok, electronics very Fiat but the base model has few enough that it isn't the end of the world. Newer Hyundai/Kia generally pretty good, but much more expensive.