There is a lot to consider here. For some websites that I've cleaned up, 27 of 87 (31%) links removed by webmasters is fantastic. Most of the time, a link from a bad site is just ignored since the webmaster just doesn't care about the website. In your case, it seems like a lot of the links that were removed came from engaged website owners which makes me question whether the link was bad in the first place.
RE effect of disavow... did your website receive a manual penalty? Or did your SEO determine that you were hit by Penguin? Those are the only two scenarios where you should be removing/disavowing links.
If manual penalty, then you will see results after you submit a reconsideration request and have the penalty revoked
If penguin, you may see results after the next penguin refresh.
Keep in mind that if the majority of your links are bad and are removed, you will probably not rank as well as you used to prior to the removal process.