The flowers are Japanese Anemones and the berries are Hypericum, Rose of Sharon or Saint John's Wort.

The White one is a Japanese Anemone,Sunnydais,and I have both this,and the pale pink one..Yes ,they do spread,but if you have the space ,they do look nice,and flower for ages....I dig out the small seedlings ,as I need to keep them in check..
The Berried plant looks very like a Hypericum? but can't be certain..

We posted almost at the same time,Jimmytheone..:o)

Specifically, I think the white one is actually Anemone 'Honorine Jobert' - the red berried plant is Hypericum inodorum, possibly one of the 'Magic' series, maybe Magic Red. And yes, if the Anemone is happy with its situation, it will spread, quite possibly more than you'd like!

Thank you!!! I managed to identify the anemone by trawling photos on line but the berry would have been harder to track down. Would probably try the Anemone in a pot first, then see how it spreads itself.

Sunny Dasies, Bamboo is not joking when she says that the Anemone will spread and get out of hand. Will be OK in a large garden but will become a brute in a small one. You can try to grow one in a pot but wouldn't be ideal in my book as it will remain too vigorous.

I found the common pink one spreads uncontrollably but Honorine Jobert was well behaved. I'd putit in the ground for a season anyway.

Agree with Stera - keep the white but jettison the pink ones.

I'll be very careful and take heed of the warnings.

I'm glad we have so many smarties on here. I nearly ran out and bought some myself. Those white ones are special.