Imperata - Red Grass - Imperata cylindrica Rubra is the main choice. Upright growing and slowly spreading grass with bright red foliage.
Iberis - The white Iberis is undoubtedly the most popular - The Common Candytuft - but there are also others worth growing - especially as they are evergreen perennials. Suit dry areas and are quite happy in dry walls or rockeries.
Impatiens - Hardy Types - As of yet, we know only of Impatiens omeana - a hardy bulbous perennial.
Incarvillea - Interesting foliage and showy exotic flowers make this an admirable choice for the border or large container. Full sun is ok, but daooled shade is better. Maybe best in wet areas to lift each autumn then re-plant in spring.
Indigofera - The shrubby or sub-shrubs are best grown in the UK.
Inula - Herbaceous perennials usually with showy yellow daisy flowers, which have long narrow individual petals. Some low growing types as well as the 2-6fy herbaceous perennial types.
Iris - Huge group of Iris either rhizomatous or bulbous perennials with varied growing situations. Some like damp and shade, other like to be baked! There is sure to be a few of the Iris group to suit your garden, and the big plus is that they do not take up too much space for the show they put on. Some have attractive striped variegated foliage.
Ixia - Mainly cormous perennials that will need to be lifted and stored for sever winters. Well worth the trouble, as it is not always easy to find many of the choice varieties at the bulb counter of the local garden centre. Once you have the ones you like, take a bit of care and help them through the winter.
Ixiolirion - herbaceous and bulbous perennials that
are mainly blue in flower with good contrasting white then yellow
stamens. Well suited to front of border or planted in containers. Full
sun is best, and not overly wet for the winter months.