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If you've removed these pages from your site then this will remove the links in Google's eyes.  (More info: http://searchenginewatch.com/article/2296653/Removing-Unnatural-Links-by-Removing-Pages-on-Your-Website).  It can take some time for this to be reflected in the algorithm.  You may be able to speed that process up by using the URL removal tool to remove these pages from the Google index. It's also a good idea to run your site through sucuri.net to look for malware as often these hackings go hand in hand with malware.  If Google has detected malware on the site then they'll give you a warning message in WMT.  Google detecting malware can definitely affect rankings. If you're not sure if you can remove the pages that these bad links are pointing to then you can add the domains to a disavow file and file that.  But really, removing the pages should do the trick.

Thanks John,I'm already working through link removals. Some of the the competition in this niche have v. poor sites in comparison (design / content) but not the thin content of our client which suggests to me that Google doesn't like the pages (especially if they're getting de-indexed now ) so I think we should look to remove these thin content web pages. I don't think losing these pages will make a massive difference in terms of traffic with the majority of these pages generating single figure visits year on year. Regards,Ade