Round and round

We went to Lytes Cary today, a small National Trust property near the A303 turn off at Podimore, Somerset. Our main purpose was to walk the dogs, so we set off through the gates, following other people!
We walked miles through open fields, partly due to a distinct lack of footpath signs!! Russet and our visiting dog Frodo had a great time, and they were allowed into the courtyard where we had a well-earned cup of tea.
I haven't discovered the purpose of this round building - dovecote ? Ice house?