Wet Garden

If you want it to be left as grass then you could try a willow, but perhaps an ornatmental twisted one that doesnt get so big as ones you would find by a river and has interetsing twisted stems in winter.

Astilbes like it wet or boggy, but they would need part shade and also the an area of grass removed to form a bed. Iris plants are also good, marginals rather than normal herbaceous ones you find in borders.
Gunnera with thier huge green leaves and 'prickly' stems, they die down in winter if you live in a cold part of england but the crown only needs frost protection. They will thrive in a boggy area.

Although if its only boggy due to recent heavy rains, and usually dries out during normal summers, then then bog garden plants as such wouldn't be too happy with this.

Is it constantly wet all year no matter how dry or wet our summers are!?

Plants suitable for bog garden conditions (all year)

Iris pseudacorus (Yellow flag)
Euphorbia palustris
Lythrum salicaria (Purple loosestrife)
Carex pendula
Gunnera manicata
Zanteceschia aethiopica (Arum lily)
Primulas
Trollius chinensis
Matteuccia struthiopteris (Ostrich fern) shady site
Rodgersia big horsechestnut like leaves shady site
Darmera peltata big leaves shady site

The Gunnera (giant rhubarb) would love there it but Id pick some willows & then coppice them every other year to get the new colourfull shoots

Go for the silver or black, or golden varieties of willows. Much more interest esp in winter

Cornus (dogwood) would like these conditions too - would give you great choice.
Lifted from BBC gardening site:-
Cornus alba 'Aurea': vigorously growing reddish stems and yellow leaves.
Cornus alba 'Elegantissima': added interest from variegated leaves.
Cornus alba'Kesselringii’: dark, almost black stems, that are a great contrast with other stem colours.
Cornus sanguinea (common dogwood): a stalwart member of wildlife gardens and hedges.
Cornus sanguinea ‘Midwinter Fire’: as the name suggests, the stems burn with fiery red and yellow tints and brighten any winter border.
Cornus stolonifera 'Flaviramea': vivid green stems when grown in full sun.

For flowers
Cornus alternifolia 'Argentea' (pagoda tree): tiered branches laden with silver-edged leaves and, in summer, clusters of white bracts.
Cornus controversa 'Variegata': also known as the wedding cake tree, with its cream-edged leaves and clusters of creamy flowers.
Cornus kousa var. chinensis: dramatic white bracts and fabulous strawberry-coloured fruits.
Cornus mas (cornelian cherry): undemanding and easy to grow with a rewarding flush of yellow flowers in spring, often as early as February, purple leaves in autumn, and edible fruits.