There is a bus that goes from Malaga to Cadiz. Its the company Portillo and I think Alsina Graells may go there too. However, it is a long journey of probably 4 to 5 hours I would guess.
I live near Estepona which is on the N340 which is the Malaga - Cadiz road and is marked by kilometre numbers. To give you an idea I live at Km 165, which is 165 Kms from cadiz and it would take me in a car two hours to get there. Malaga is an hour from me in the other direction, so allowing for a few stops on the bus and the fact they don't go 190 Km per hour (neither do I, just joking!) it is a long journey by bus.
You can get the train from Malaga to Sevilla and go that way. Whichever way you choose, it'll take you a few hours to get there but the scenery is certainly different from Cheshire and will be interesting. Hiring a car as a timid driver who is used to the other side of the road may not be a good idea, as although the roads are good and well signposted in the main, it can be a bit nerve-wracking in new cities if by yourself.
Tell you what, why don't you check out Marbella first? Get a bus direct from the airport to Marbella bus station, non-stop, leaves regularly and then you can break the journey if nothing else. On the other hand Marbella may tickle your fancy and that's where you end up. Otherwise, get a bus later from Marbella to Tarifa and look round there too. From there it's just a couple of hours to what may be your final detination of Cadiz.....or not. Whatever, have a good trip!
_________________________
Fantastic apartment to rent from less than $50 a night!!
www.spainrenting.com