Thymes are nice for this and you get a lovely aromatic scent when they are walked on, they will also spread a little and soften the edge of the paving. Aubretia is lovely too, but it may spread a bit to much for paving, bit a couple of plants would be worth a try.

Mix lots of grit in to the soil when planting them, they are better with good drainage.

you could also try Chamomile which smells nice when walked on, other possibles could be Acaena (some are invasive), Sagina subulata or Paronychia. Is less trodden areas you could add a few dwarf pinks or Campanula cochlearifolia.

Why not try some cement carefully applied between the stones. This will preserve the stonework, delay spending several thousands of £ and remain an asset.

Patios are good places for chairs, tables and pots. Flowerbeds are good places for flowers, herbs and weeds.

Moriati

Acaena (Australian Burr> and the smaller New Zealand Burr would look fine here - evergreen, hardy, small white flower balls and dark red seed heads which can persist all winter - BUT - the seeds have masses of very fine hooked hairs, which cling to everything, and can be walked into the house. They can cause skin problems - piercing the skin - especially children and animals. Our dog had an eye ulcer caused by one of the hairs - cost us £600 for treatment.

erigeron karvinskianus - mexican wall daisy.

As grass is doing well, what about some short ornamental grass like Festuca Elija blue, or quaking grass? Some flowers will self seed and come up yearly, such as alyssum and violas.
A little story about this - where I work the building is in the form of a square and enclosed a courtyard with paving with some tubs of flowers. For safety reasons the gardeners could not go in the courtyard for about a year, so weeds grew between the cracks, including self sown mimulus. Finally the gardeners could go back in, and they weeded and pressure washed all the paving. About 6 to 8 weeks later the cracks were all studded with little red and yellow mimulus - very pretty!

Cotula perpusilla 'Platt's Black' might suit. Beware of Laurentia fluviatilis. I'm sure it has dreams of world domination.

how do you manage to keep Laurentia fluviatilis alive? I have tried growing it a couple of times now and it has always died within a few weeks. Beautiful little plant though, might have to have another try...

My mother has it growing rampantly in bark chips and it is walked on regularly. It gets morning sun and afternoon shade. Well-drained but with moisture retention.

Mine grows in gravel - about 7mm sharp with leaf litter mixed in - where it gets some run off from a gravel path, early sun and afternoon shade. I thought it might give it a touch of restraint. It thought for a season and is now burrowing underneath the Chamomile 'Treneague' which also shares the gravel.

Before that it lived for some time in the squalor of a strawberry punnet - shallow soil, excellent drainage and infrequent water, though only morning sun. Once you've got it going it's a stayer.

Both gardens get light frosts 1-5 degrees. A 'good frost' is one that puts about quarter of an inch of ice on a pot of water and is mostly gone from all but frost sinks by lunch time. They're not common.

Both gardens can get very dry over summer.

There is a bristly moss (at least I think it's a moss - it might not be) that grows in the narrowest of cracks and spreads an inch or two beyond, and can be walked over daily, and swept with a hard broom. It grows in my back yard in full sun. Same colour as grass but stays under 1cm high. Have a look around other paved or concreted sites in your locality. There are also some very tiny Oxalis that grow and flower in tight paving crevices.

For shadier cracks alongside walls, there is 'Mind-your-own-business' Soleirolia soleirolii (syn. Helxine
soleirolii) which some dismiss as a weed but which I like and encourage. Also nicknamed 'guttercress' it has very tiny bright evergreen leaves on very thin red stems. It will tolerate being knocked about but won't grow out in the middle of paving.

Berl

I also have York stone. Things which have arrived by themselves are:

Erigeron as mentioned above (formerly E mucronatus)
Campanula porscharskyana
Campanula portenschlagiana
Wildsteinia ternata
Cotoneaster horizontalis
Chives
Foxgloves
yellow corydalis
Dandelions (!)
I have also had success pushing crocus bulbs into the cracks. In my present garden they are large white Dutch crocuses but in a previous patio I had C. tomassinianus self seeding.
I have failed repeatedly with thymes.

Isn't there a nice little mint that would be suitable for paving? I can't remember what it is.

Claire, I wonder if you mean corsican mint, mentha requienii, or pennyroyal, mentha pulegium. The book I'm looking them up in says the corsican grows naturally in cracks in rocks and is suitable for paving paths.

I had a few plants which just turned up in cracks between paving in my front garden, most of which I weed out, but those I encourage include some kind of libertia. Flowers seem quite short lived, but the foliage is evergreen and looks good the rest of the year, save for the occasional brown leaf. Grows about 18in high or more, though, so it's not the kind of low growing plant you're looking for in general. In my back garden, I have the harebell, campanula rotundifolia growing in cracks in paving which grows to around 6in high. Not as delicate as it looks, and some of mine got bashed around a bit by accident earlier in the year and recovered, though I wouldn't (deliberately) walk on it.

I'd be wary of oxalis unless it's a kind you're sure is not too invasive. My mother has some kind of bronze-leaved oxalis in her patio paving - looks pretty with yellow flowers - but it spreads everywhere, all over her lawn and borders as well. I know some of them are OK, I have oxalis deppei 'iron cross' and that's no trouble, but that's not suitable for paving.

Creeping thymes work well for me among pavers, but make sure they are really lowgrowing. I had success with some from a T&M packet years ago but can't remember the name. The drawback is that it attracts bumblebees and wasps when in flower. 'Elfin' is a variety without flowers.