No photos being stored locally on phone

On my iphone 6s no full resolution photos are stored locally.

Almost immediately after taking a photo it is uploaded to icloud, and when I go to look back through the photos, they each have to be loaded separately. It is frustrating, as if I want to show someone a photo I took yesterday, it has to pull it down from the cloud each time, while i stare at a low resolution thumbnail.

And once the full res version is downloaded to the phone, it disappears again after a short while.

There is no problem with storage on the devices. The phone has 20gb free (of 60gb). So it is not like the os is optimising to save space.

The photo library is large - 40,000+ so perhaps this is a factor?

The phone has 5.6gb stored on the phone. Which I guess must be thumbnails.

I thought that the most recent photos would at least remain on the phone so that i am not constantly uploading and downloading images...

Anyone else have this problem?