Looking at the RHS website, the following seems to suggest that your honeysuckle falls into the first category, so spring would be the time to tidy it up:
Honeysuckles flowering on the current season’s growth, such as Lonicera japonica (Japanese honeysuckle), do not require regular pruning. Simply control the growth by cutting back any overlong shoots in spring. Also thin out congested growth and remove weak or damaged stems.
Honeysuckles that flower early in the season, on short side shoots on the previous year's growth, such as Lonicera periclymenum (common honeysuckle), should be pruned back by about one-third in late summer immediately after flowering.
Renovate climbers by hard pruning to 60cm (2ft) from the ground in early spring. Thin out vigorous re-growth and tie in the new shots.