We bought our daughter a Skoda Fabia, hers was brand new but they had some bargains on the same forecourt. It has been brilliant - first year newly qualified driver 1200 quid comprehensive , second year 800, good mpg ratio, cheap tax .
If you want free tax - buy a pre 71 classic and get cheaper insurance too
Suggestions include an Austin 1100/ 1300 if you can find a good one - another advantage of this is the fact that the car will appreciate in value too
Alternatively (again pre 71) MGB
I think the best car on the road for new drivers are Corsa's. I have owned two, my mother still has hers and has done now for 6 years.
I think Vauxhall are currently offering free insurance for certain drivers too.
They are only group 2 insurance (providing on model) and the fuel consumption is great. The Corsa won't depreciate as much as a Saxo, 106, Punto, Ka or Fabia.