I want to plant a climbing plant in a container on a north facing wall. It must be evergreen and if possible flowering.

Garrya elliptica grows well on a north wall. It doesn't actually climb but likes a wall at its back. It has long grey/yellow tassels all winter and evergreen leaves. Clematis cirrhosa 'Freckles' flowers in late winter and is evergreen. Don't bother with Hydrangea petiolaris as it won't flower very well on a north wall despite what the books say.

Variegated euonymus are evergreen and, although the flowers are practically negligible, the leaves make up for it. 'Silver Queen' and 'Emerald Gaiety' are two good ones. They are self clinging but not aggressively so

Clematis Armandii always works for me, it has gorgeous long shint green evergreen leaves and white sweet flowers in the Spring. There are types of climbing pyracantha which produce a profusion of berries which grow flat against a North facing wall. There is also a Fathedra Lizzei (Fat headed Lizzie) which is a cross between Hedra (ivy) and Fatsia Japonica, I am trying this against a North facing wall as well as a Garrya Elliptica

My H petiolaris must be the exception then, Volunteer!!!

I also have a Clematis 'Nelly Moser' there which seems OK.