A lawn can't really be called a lawn if there are no daisies.
I have a few patches of daisies, but they are only visible in places where the grass has not been cut for a while....
The heads are perhaps 4 inches above the ground level, so if you cut the grass at all short or regularly, then you're liable to cut the flower heads off.
I wouldn't have thought that daisies are difficult to propagate or establish.
The RHS provide a service that lists nurseries that can supply any particular plant. There appears to be just one nursery that supplies daisies (Bellis perennis) by mail order.
It's this one: Arne Herbs
Putting Bellis in their search box finds the plant. They say:
"Native species detested by modern whatsit-retentive lawn enthusiasts, but deeply loved by Medievals."
You need to E-mail them to see if the plant is in stock. Or you could scrounge another plant from a friend or neighbour.