Hi Carl,
First step is to identify all of the links. Pull off the full backlink data from OSE, Majestic SEO, Ahrefs and WMT. Compile all of them into one master spreadsheet and then upload these to the Link Detox Tool (http://www.linkdetox.com/). This will give you a starting point for finding all of the toxic links - bare in mind that this is just a guide and you will still need to go over the link manually.
Start gathering webmaster details and record EVERYTHING in a Google Docs spreadsheet. Record the webmasters' contact details, URL, date you contacted them, the date of the response, any action taken, etc. Spend a good month on link removal to get as many removed manually as possible.
Once this stage is complete you will need to Disavow the rest of the links. Be careful here not to Disavow genuine good links. When it comes to the likes of SENuke links, you will want to Disavow them on domain level, i.e:
domain:jonnyhetherington. com
After you have submitted a Disavow, submit a reconsideration request and let Google know all of the bad links that were pointing to the site, why they were there and what you have done to rectify it - be explicit. Also, link to the Google Docs spreadsheet with all the details in.
If you get a negative response back then dig a little deeper with the links to Disavow - most reconsideration requests get knocked back the first time but ignore those that say 'you can't recover', because you can. Just make sure that your client understands the implications of everything. They will have further dips in rankings and traffic before it gets better.
Hope this gives you a good starting point.