A true English garden has something flowering at all times of the year. Most perennial plants are done blooming by December, but there are shrubs and vines that can sometimes give you scent and flowers during the winter. Some of them are only hardy in warmer climates.

Jasminum nudiflorum or winter flowering jasmine
This is a lovely winter climbing plant which needs to be trained on wires or a trellis, as it is not self-clinging. It has cheerful yellow flowers, which give off a marvellous scent.
The flowers appear on bare, bright green stems throughout the winter and into early spring.

Clematis Snowbells
This vine has soft creamy/lime bell-like flowers from December through to March. It prefers free draining soil and will do well in a sunny spot or a part shaded one.

Mahonia japonica or sometimes called Oregon Grape Holly.
It is an evergreen shrub that's sometimes mistaken for holly because it has large spiky, leathery leaves. It flowers from the beginning of December to February.
It has a strong scent. The flowers can be deep yellow through to the palest lemon yellow. These are followed by blue-black berries.

Sarcococca confusa or sweet box
Sweet box has a very sweet vanilla fragrance and blooms from December to March.
It is an evergreen shrub that likes a shady spot at the back of the border.
It is easy to grow even in dry shade.

Viburnums
There are several deciduous winter flowering shrubs that will flower from the end of November through to early march.
Viburnam tinus, Viburnum farreri, Viburnum bodnantense, Viburnum'Dawn' and 'Deben' are easy to grow. They tend to grow into quite upright shrubs and like a sunny spot with well drained soil. Most have white flowers followed by blue-black berries.

Helleborus niger or Christmas rose
This lovely winter flowering perennial comes in a range of pinks, whites, green, and dark purple black. It has saucer-shaped flowers and blooms from late December through to March.
Plant them in a sheltered spot away from strong winds. It was thought to have been brought to England by the Romans and used to be planted close to cottage doors because folklore said it prevented any evil spirits from entering the home. They are deer-resistant too.
Try Helleborus purpurascens which is a lovely purple flowered hellebore that flowers just before Christmas.

And don't forget winter flowering pansies which will give you flowers throughout the long winter months!