Patio

I don't think so, considering weather and traffic problems. However, there is a product on this side of the pond that can be painted on. It's tiny little granules of granite in some kind of liquid base and comes in several natural-looking colours. I've used it over concrete, with good results. I believe it started as a slip-resistant poolside coating. I'll see if I can dig up a website.

Here's one product:

Beautistone

You can maybe check out if your local hardware or paint supply store has something similar.

I looked at the website, Tico. Interesting but I think I had more of big square flagstones in mind. Clever what people come up with, isn't it.

Well, in my experience, many people put stone over existing concrete, given the existing concrete is built correctly - drains in the right direction, has proper scorelines and expansion joints, appropriate depth, and, if in California, has appropriate amount of steel or equivalent.

Whereas one might put two to three inch depth of flagstone over soil and base, one could put thinner, say, 1" thick, over concrete with mortar. People do that with brick veneer too. Or, stone tiles, or terra cotta tiles, treated to be non slippery. But, I think terra cotta would look silly in England, just as it would in my last place at the very north of California. There are faux stone tiles. Lots of possibilities.

Given you use tiles, they'll probably be of an equal depth, but with cut stone, you need someone who knows what they are doing re the laying of it. I think you need someone who knows what they are doing anyway.

Check around a lot before you do it, people vary in their abilities and their tastes - and certainly in knowledge and competence. Looking around is time well spent.

I gather we have to have the present crazy tiling removed because otherwise it'll be too high for the damp proof course.

All good advice you've given me, ossobuco. Many thanks.