Is there any hope for this?

[Paddingtonthebear]

Ancient patio. Had a quote to replace it but it’s ££££ Is there any other way of making it look better?

if it's all sound - ie nothing moving I'd just clean out the grass and then get it jetwashed by someone who knows what they're doing (so they just clean the stones not disturb them).

Is it at the front or back of the house I’d agree on cleaning it up, but then decide what look I’d want. You could build a frame and fill with gravel.
Personally, if it was at the back I’d plant something like thyme or camomile in the crack. Weeds and grass will grow back in the cracks if they’re left empty. I’m a bit of a shabby chic style of gardener.
Otherwise just keep jet washing it.

Yes back of house, 28sq metre area

Personally I’d just jet wash that and kill the weeds and moss. You don’t need a professional it’s not difficult. You can then either regrout or get a quote for someone to do it

What is your desired outcome? No grass? Clean slabs?
Do they move or are they stable?

Personally, if it was at the back I’d plant something like thyme or camomile in the crack. Weeds and grass will grow back in the cracks if they’re left empty. I’m a bit of a shabby chic style of gardener.

I agree with this, you won't get a clean / sleek / modern look with this patio no matter how much you jet wash it, so I would also go for a vintage / shabby look with thyme between the cracks and lots of nice glazed ceramic or terracotta flower pots.