Its south facing full sunshine from about 11am until about 6pm. It's also under a glass roof so they need to be ok if I forget to water them occasionally (although the windos box is outside the kitchen window and so hopefully that won't happen too often).
The combination of sun, glass, pots and dryness screams 'Go for drought-tolerant Mediterranean herbs!" Things like thyme, oregano, rosemary, sage, lavender. You can buy tiny plug plants for next to nothing and they will grow really, really fast. Think about mixing some horticultural grit into the compost when you pot up and make sure they do get a bit of water occasionally - even drought-tolerant plants need a drink sometimes!
I've just planted a lavender hedge along the edge of the area which is shooting up and filling out really nicely. I'll go and get some thyme, oregano and rosemary if they'll do well. I am hoping for scent as we brush past as well as being able to keep the kitchen stocked.
I didn't realise I'd need grit so thank you for the tip.