I'm sure it is possible in theory, but it would have to be a VERY big pot, and you'd have to do some fairly heavy duty watering throughout the year. The trouble with growing things in pots is that the roots are far more vulnerable to being "cooked" in hot weather and frozen in winter (not that I think the winters in the Costa del Sol are too bad), and will dry out very quickly. Would it not be possible to plant it in the ground?
I'm really not knowledgeable enough about vines to recommend a particular one, and it will depend on what you want it for - shade and decoration, or for the grapes themselves, but I'm sure there will be someone on here who be.

I would have thought it got far to hot in summer for a grape vine to grow and certainly not in a pot.

Well, they grow them here down in the valley, against house walls and as crops (not up here - too cold in winter) and the temperatures reach the high forties, but against any wall, especially a south-facing one, in that sort of weather, the reflected heat alone wouldn't be good for it. I think the pot idea is a non-starter.

Vines like a lean chalky soil if at all possible and sink a tap root metres deep to look for water.

I was going to suggest a fig tree, but I've now read what you say about the depth of concrete. I am at a loss what to suggest. If you are away for any length of time, you are pretty much going to lose anything you try planting in a pot. How about a nice mural? ;o)))

How about a citrus tree? It's obviously not a 'climber' but once established they seem to look after themselves, then you have the added bonus of reaching up from your bed in the sun for a lemon to go in your G&T. ;o)

Even citrus trees, if planted in a pot, however big, are going to need watering, Nariz, inviting though that G & T sounds!

I think Gattina's mural is the solution! Any plants in pots against south facing walls in temps of 40˚C will need a lot of tlc.

Thought I'd mention it as we stayed in a little townhouse in Andalucia earlier this year which had a lemon tree - complete with lemons - growing in a patch of earth on the patio where a paving stone had been lifted to accommodate it. Being a rental house I doubt that much watering took place and it must have relied on whatever rainfall reached it - along with the 'Money Tree' in a large pot which also looked healthy.

Someone could have been going in and watering on a regular basis Nariz

I think you are right, MG. The money tree sounds like an idea, Nariz, but they don't grow particularly big, do they? You can, in theory, grow quite large olive trees in pots, but the pots themselves have to be almost big enough to set up home in and will cost hundreds of euros. It's probably not what you had in mind.