The hosting providers got back to me and came up with what I have found:
"I have had a further look into this and unfortunately, I was not able to find where the redirects are coming from in the site this time around, do you know when the site was last working correctly before this started redirecting?
I ran a few searches for the links which seemed to have come up empty and only false positives being flagged up when searching for other typical malware."
I have found that two scripts are running on the site: apu.php and banners.js - but both of which are not on the server, but are being run from another site ("go.onclasrv.com/apu.php?zoneid=676655" and "eclkmpsa.com/adServe/banners?tid=79479_131506_0&tagid=2") You can see the code for these by following the inks.
I can't believe I am the first person to encounter this problem...?