Kate, How are your corners/ends of fence braced? If you go to the effort of re-stretching the fence, well braced corners and ends (gates) will help keep it from sagging again. "H-bracing" seems like it is best, but also an angled brace is another method.
Are your steel posts the "T" style posts? Here in the U.S. there's some manufactured bracing fittings for those... also pre-formed wire clips for holding the woven wire...
Wire ties to the posts doesn't sound so bad, easy to release the fencing with diagonal cutters... Here in the U.S. there is a second style of steel post, stamped sheet metal, that has little hooks that one crimps/hammers shut over the fence wire. Hooks down low point down, to prevent lifting the fencing, hooks on top the opposite to hold it up. All the hooks you don't use grab your fencing in ways that aren't helpful at all... and the hooks rarely survive prying open and a second crimping.
There's all sorts of gadgets for wire tying... for fencing,
concrete rebar, and safety wire twisting pliers... some that might be a labor savings over hand twisting with pliers, especially the methods with pre-made ties.