To get an idea of what car you can get at that price that suits your needs, have a look at:
http://www.usedcarexpert.co.uk/buy/-/price/from-5000/to-7000/postcode-ls11+0es/type-small+family+cars/transmission-automatic/doors-5/order-distance+low+to+high/I'm doing some work for that site, and spoke to someone who test-drives a lot of the cars for the reviews, etc.
He said:
Renault is silky smooth
A golf always looks good but is dull
Kias and Citroens are to be avoided
Mazdas are fun to drive
Fords and Vauxhalls are cheap to service
So you might want to consider what he says (or not) when making your decision. It's definitely worth driving a few to see the difference for yourself, and checking out the space they have (and access is also important too, a big boot is no good if the opening is too high or narrow, etc.).