For £6k you could get a brand new bog standard Dacia Sandero, but that is about the only option for a new car unless you trawl through the car brokers/ car supermarkets (where you might get something a little more appealing). And bear in mind it will be white, it won't have a radio, and you will have to wind up the windows yourself!>

As for used. You say medium sized, i'm assuming that means VW Golf/Ford Focus sized?. I don't think there is any need to go for anything bigger (such as a Honda Accord).

So, in no particular order, my suggestions would be (along with the youngest example you'd get with >70k miles for your £6k)

Ford Focus 1.6 2014.

Honda Civic 1.4 or 1.8, 2013.

Toyota Auris 1.33 or 1.6, 2013.

Mazda 3 1.6, 2013.

Kia Cee'd 1.4 or 1.6, 2014.

Hyundai i30 1.4 or 1.6 2014.

If you want a higher seating position,

Kia Soul 1.6 2014

Kia Venga 1.4 2016

Hyundai ix20 1.4 2015

Ford C Max 1.6 2014

If you think you could manage with a slightly smaller car,

Toyota Yaris 1.33 2015

Honda Jazz 1.2 or 1.4 2015

Kia Rio 1.25 or 1.4 2016

Hyundai i20 1.25 or 1.4 2016

All of those suggestions are inherently reliable, but obviously there needs to be evidence of having been looked after (service history). Bear in mind that Kia's come with a 7 year warranty, so assuming a proper dealer service history, that 2016 Rio will still have 4 years warranty remaining. Hyundai's have a 5 year warranty, so even the i20 will still have a couple of years left. Current Toyota's have a 5 year warranty, but i'm not sure when they changed to 5 from 3, but they are very, very reliable. I have not mentioned the Mazda 2, as while a cracking little car, your budget being what it is would only stretch to the last of the previous style, which will probably be a little small for all your stuff. The Honda Jazz has an amazing amount of interior space along with a boot closer in size to a Focus than a Fiesta. it also has Honda's brilliant 'magic seats', where the rear seat bases fold up to reveal a large space which can be used as a 2nd boot behind the front seats for taller stuff.

Have you just passed your driving test? Then your insurance costs will be sky high. You need to work backwards, get insurance quotes and then see what you have left over. You should get quotes for comprehensive insurance and legal cover. You need to allow for servicing costs and parking costs etc...

When I passed my test, I was a nervous driver, so can you driver with distractions such as children in the back and lunatic drivers, cyclist etc,,,?

In London there are a number of car clubs, which may be appropriate. They are expensive, but can work out better in some cases. You need to read the small print. Some include fuel and insurance. You will get newer cars. That combined with Uber etc... it might just work for you, depending on the journeys you want to make.

A £6,000 car, will loose about £900 per year in value.