Jasmin

Summer flowering true jasmine (rather than winter jasmine or star jasmine) grows like a weed, so will take hacking back.  It is usually so thick with stems it is difficult to prune it any other way.

Take the front off and hack back until you get the width of plant you want.  By that stage, quite a lot of the top growth will have come off with what you have already cut.  You can then see what further top growth you want to remove.

I remember helping a friend who had just moved into a terrace house.  She had Jasmine all over her narrow back garden that she thought had escaped off her fence.  Turned out the plant was in the next door but one garden and it rapidly turned into a work party with her neighbours.  Everyone got their gardens back and rooted plants next to fences if they wanted them 

If you cut out the weedy growth down to ground level, it will put all the energy into the main branches and they should sprout a lot of new growth.  For a dense bushy plant for birds to nest in, that wouldn't be a bad idea.

If the main branches are thick enough to support the weight of the plant, it not being tied to the fence shouldn't be a problem.  Just watch it doesn't come out too far, making the plant top heavy, as it could go over eventually 

If you put up some vine eyes and wire on the fence at a couple of levels, you can tuck the new growth behind the wire as it grows. An annual clip over the front will help keep it under control higher up.

It is an excellent plant imho and well worth rejuvenating