Salix varieties (willows) though I wouldn't recommend a full size Weeping Willow (Salix babylonica). Any of the others will do, but some, like the coloured bark types such as Salix alba 'Chermesina' or 'Vitelina', you need to stool regularly. If you don't mind a reasonable sized tree, Salix tortuousa is attractive.

what about plants like filipendula, astible, hosta [if not in full sun] they all like damp conditions.

Viburnum opulus,(there is a dwarf one that only grows to 5feet or so and has red berries, or the tall "snowball " one that is sterile. Cornus alba, & berberis all tolerate wet ground.

gunnera is nice

You might want to find out why it is very wet first. Is the wetness due to geography (the dip in the ground), geology (clay subsoil perhaps) or a leaking water pipe?
If I've got the directions right you have a damp area with the shade of a fence throughout most of the day - I'd go with SBG's selection of perennials plus ferns, epimedium, yellow foxgloves, brunnera macrophylla.......... with Cornus and pulmonaria rubra to give a bit of winter colour.

Is it wet all year round? Why not go all out for a proper bog garden - sink a pond and create a little nature reserve.

If it's damp rather than wet, then clematis and honeysuckle might appreciate the shade and will give a bit of interest to the fence, which could also get a coat of coloured paint, if it hasn't already had one.