Our native common honeysuckle, Lonicera periclymenum, is the best for fragrance in my book. Honeysuckle Halliana has a good perfume as well as very nice cream and yellow flowers.

Honeysuckle is not strictly speaking a climbing plant it does need something to grow on and will need to be tied in to it. Sorry I live too far away to recommend a variety but generally speaking I'd agree with Pimpernel. Sorry I'm not an expert.

Erm, that's not really true, Scotsgran - a large section of the honeysuckles are climbers or scramblers - they twine round anything they can find to get up. The rest are shrubby.
If I were choosing for fragrance, I'd go for Lonicera Belgica, which flowers early, AND Lonicera Serotina, later flowering - both highly fragrant, and the latter one starts flowering as Belgica finishes, both with very attractive to look at flowers too.

Honeysuckle Periclymenum is Belgica so you might find it under either name.
I copied this advice on care of honeysuckle from the Van Meuwen website so Bamboo is correct but they do need something to hold on to.
"Caution: Harmful if eaten. Grow honeysuckle in sunny or semi shaded sites in any moist, well drained soil. Prior to planting add plenty of well rotted manure or garden compost to the soil. Be sure to provide the twining stems with an appropriate support, such as trellis or wires attached to fences and pergolas. Alternatively grow honeysuckle through shrubs and trees."
They now sell a winter flowering one L. purpusii 'Winter Beauty' so you can extend the perfume further through the year.

Erm, sorry, Scotsgran to be pedantic, but for the purposes of getting the right plant, Lonicera periclymenum is not the same as the variety 'Belgica' - that's a specific cultivar of L. periclymenum, so not exactly the same as its parent.