I'd add extra boards to the fence on the inside so that they are placed over the gaps and have their own gaps not in line with the gaps between the outside boards. In this way you will still have a fence that has reduced wind resistance but will achieve privacy.

This will also be instant, unlike ivy which sits for a couple of years and then goes ballistic. If you get the timber from a builders merchant and ask for a price first it shouldn't be too expensive either. There's an art to buying from builders merchants but it's the way to go!