It's a lovely idea but might be very hard to carry out. Did you see the BBC progamme on the South Downs recently?
It explained that the chalk grassland depends on close grazing at the right time of year to maintain it, and some of the plants that make it so special are things like orchis, most of which are unavailable commercially and very difficult to raise from seed (if you can get it!)
This web site gives you some information about downland and the plants that grow there.
Many of them would grow well in a small rockery, or scree, forgetting the meadow as such, and would look very pretty, so you could make a container for that and site it somewhere sunny. It wouldn't need to be very deep, as limestone soils are thin. Limestone chippings will give you an alkaline environment, but I think they are harder and break down more slowly than pure chak, so you would need to choose small sized ones. You may find a few of the plants available in nurseries, or a good seed merchant such as Chiltern Seeds will be able to supply them. (There may well be others, this is just the one I use!)
Hope this will help you get something of the effect you want