It depends on how attached the ivy is.

If it has grown through the fence in places you'll have quite a job removing it using secateurs or a sharp knife to cut off the stems.. If it is just growing up the fence you may well be able to remove it using a decorators scraper to remove the suckering roots by which ivy's attach themselves to things.. I have also removed ivies off walls using a spade. Just sliding the spade from the top of the ivy down the wall and the roots come off quite easily leaving the stems undamaged.

If you manage to get the ivy off the fence largely in one piece you'll then have to securely reattach it .

Having said all this it will be quite a task and may not look very good when you've finished.

If you can't get a look you're satisfied with all is not lost as well established ivy can grow 6 feet a year so you could cut it off near the base and it should recover the fence in a year or two but it will take longer than that to be thick enough for large birds to nest in it.

Thanks for that, I was thinking along those lines but wanted confirmation before I started.

You can also use a half-moon lawn edging tool to scrape ivy off of walls