I have two honeysuckles, in my last house I had one growing up and over a pergola, every 3 years I hard pruned it down to about 12 inches to the ground to rejuvenate it and it buds at the bottom from that point otherwise it gets too leggy and you get all the flowers at the top and none at the bottom.
After its finished flowering is best. If its really badly overgrown wait until winter to cut it back to a metre. But if you do this it will not flower the following year. We do not cut ours back very much we do some pruning after its finished flowering and then again in early spring.
Kate you can cut out the dead wood if you wish to. Keep deadheading the flowers to get more and trim back non flowering shoots by a couple of leaves. Ours flowered twice and is still flowering in september.
