I found this checklist of invasive non-native plants to avoid, if it helps:
Australian Swamp Stonecrop, New Zealand Stonecrop, New Zealand Pigmyweed (Crassula helmsii)
Canadian Waterweed or Pondweed (Elodea canadensis)
Curly Waterweed (Lagarosiphon major or Elodea crispa)
Fanwort (Cabomba carolinana)
Floating Pennywort (Hydrocotyle ranunculoides)
Giant Salvinia (Salvinia molesta)
Green Seafingers (Codium fragile)
Lesser Duckweed (Lemna miniscla)
Nuttall's Waterweed (Elodea nuttallii)
Parrot's Feather (Myriophyllum aquaticum or Myriophullym brasiliensis)
Water Fern (Azolla filliculoides)
Water Hyacinth (Eichornia crassipes)
Water Lettuce (Pistia stratiotes)
Water Primrose (Lugwigia grandiflora)
Maidenhead Aquatics had native species when I went - you should have an idea of possible species in mind before you visit a Water Garden Centre .
I use Hornwort as an oxygenator and I also grow Water Soldier, Water Starwort, Frogbit, Arrowhead and various rushes (some native) and irises. The irises I have are not native (too large), and I certainly wouldn't recommend the larger, native "bullrushes" - these are not suitable for a small pond. Try and find some smaller emergents. Do not introduce Duckweed, native or not!
