Hi Busybeemum and welcome to GoY. You need to be growing plants that like alkaline soil, and plants that can grow in a poor soil too. The Mediterranean herbs such as thyme and marjoram will do well as should
Echinacea purpurea
Rudbeckia fulgida
Lavandula angustifolia 'Hidcote'
Centaurea cyanus
Papaver australis 'Perry's White'

...Clematis, Dianthus, Verbascum's & Scabious love it too, to name a few more.

Shrubs could include Buxus or Taxus if you wanted to edge your borders with a low clipped hedge too.

welcome to goy.
i garden on chalky soil with some sun and lots of shade. Have a look on my garden profile to see what I grow.

Poppies seem to do well on chalky soil.

Bearded Iris (all sizes), and Origanum species.

Thanks ever so much for the plant tips, i'll try & plant a few & let you know how they go :) x