I think that the global impact was down to DNS servers being taken out - DNS caching kept most things going, but the outage was so long that by the end of it, cached entries were starting to expire - and presumably the least-used ones went first.
In my case, email stopped working, and I found that the name of my mail router wasn't resolvable on Virgin Media's DNS servers. However, it was still OK on Google's DNS service (8.8.8.8), so I switched to that. I tried dnschecker.org and found that my mail router wasn't resolvable on roughly half of the randomly-selected DNS servers - but e.g google.co.uk was still resolvable on all of them