Cape leadwort

Technically a South African shrub, it's typically treated as a climber and is best grown against a conservatory wall. The sky blue flowers (though there is a white version) appear at the ends of the whippy new growth, and last from summer to autumn. If it gets out of control, prune hard in spring and it'll send up a mass of new growth. It can be grown as an annual outside, but cut down and bring into a frost-free greenhouse over winter for planting out next spring. It has been given the Award of Garden Merit by the RHS.