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Thanks. I had the feeling i was probably getting a bit carried away. I've been working so long at the link removals now, and I'm worried if I leave anything spammy we'll be stuck with this Penguin penalty forever, but I'll just ignore these links.

One sneaky trick that your competitors don't want you to know about... I could really use that headline with this. Imagine things this way, you are doing backlink profiling on a competitor that ranks above you. You see that he has a bunch of spammy forums posts. But no matter what you do, you cannot out rank him. So you start forum spamming yourself to try to catch him in the SERPS. But then you get a penalty. The disavow tool has more than one use really. It will let Google know not to penalize you for links (or give you credit) but it will also mask your link profile too. I would just disavow them and be done with it. Let you competitors try to figure out what Google is giving you credit for or is not.

Yes, that's generally considered the correct way of doing it if you have links to both www and non-www.

Thanks, Marie. That's a big help. It's your third point that I'm most worried about. Not all of our backlink profile consists of spam. We have some really good links - from the BBC, various other UK media like the Guardian, the Independent, even from wikipedia - but these links are mostly years old, and there isn't that much beneath them. We have a handful of good links at the top, and then a whole mass of spam, with very little inbetween. By the time I finish disavowing, there will probably only be about 30 or so legitimate domains pointing to ours. Google used to rank our website well,  even before we employed an SEO. We've kept some of these rankings, particularly in image search*, so I've some hope that we'll make a recovery from penguin in other areas, but I also know that penguin hits can be permanent. *This is, or rather was, our one bright spot, even after penguin hit us. You used to be able to type in just about any region or game park in Africa - our main business - and our images would come up first in the results. We lost these rankings not with penguin but when we changed our website dimensions a year or two ago and had to upload new images to replace the old. Those that we didn't change still rank well - type in Serengeti, for instance, and we're still right at the top. I've never been able to understand why we do so well in image search and so poorly in the main search results. Not sure if there's a question anywhere in there. I think I'm just waffling now. Thanks again for the advice.

Travis, your comments are a massive help. Thanks so much. That Screaming Frog tool is also really helpful. I had noticed that different backlink checkers were giving me different results, and so I've been working with several (Webmaster tools, webmeup, Moz, and ahrefs) Originally, i was just working with webmaster, and so it was something of a revelation when I first looked at the data provided by the others and found that there were about five times as many spam links pointing to our site as I had first suspected. I think many of the sites pointing to ours have been deindexed, so won't show up in webmaster tools. I had also noticed that recent reports I'd generated were picking up on far fewer spam links than older ones, despite me not having managed to get rid of that many links. The post from Robert Fisher helps explain why. With most of the links I'm deleting, I think they're clearly spam. The seo company we used depended mostly on article directories, but also some forum and comment spam - some on legitimate sites, most on forums that were clearly just created for SEO spam. What I'm thinking is that I will focus on deleting the links with the most repetitive anchor text, and leave a few of those with more varied anchor text. From my understanding of penguin, google doesn't so much penalise you for having a large number of links from spammy sites - it penalises you for having a large number of links with identical anchor text, so I'm prioritising those links with keyword rich anchor text ('Tanzania safari', in our case) and leaving in place for the time being some of the smaller number of links with less repetitive anchor text (a small number say 'trips to Tanzania', for instance). The content audit looks like a mammoth job, but I'll try and work on that this weekend. I know that our site has a lot of duplicate content, for one thing (in some cases for good reasons). Perhaps we've been hit by panda as well as penguin. Thanks again.