Could be Cuneatum or Erectum

The more commonly grown one that fit the pictures, Vincent, would be Trillium chloropetalum for the red ones and T. albidum for the white. There are more unusual species which 'could' match the images.

Hi, I would agree with Scotkat, T Cuneatum for the first photo, and T Grandiflorum, {possibly flore pleno}, for the second, Derek.

Great pictures btw Vincent

Thanks folks, taken with my phone, Andrew! My camera had run out of battery. I have put them on 'Dave's Garden' to see if anyone in the U.S. might be able to spot the differences between the species. I have no reason to suspect that they are that unusual.