There's also a story at The Telegraph that we at Virgin Media contributed to, as we definitely saw a rise in traffic after about 11PM but it was well within the fluctuations we capacity plan for.
On our core network (that's everything IP beyond the Cable Modem Termination Systems - the devices our cable customers' cable modems), we experienced a 10.8% growth in traffic last night.
Having a look at one of our network graphs (for transit traffic), you can see how traffic continued to grow until midnight whereas on a normal evening (such as the one before) the traffic is tailing off in the late evening:
We didn't experience any interruption to service though. As is often the case when stories of a large magnitude break the bottleneck was more at the other end of the connection with various websites experiencing downtime under the weight of demand for news rather than the ISP networks being affected.