If you've ever read the ICO documents on what constitues personal data ( A rather dry read) then you should know that Personal information is anything the can be just to uniquely identify an individual.
So saying my name is Fred Blogs is not classed as personal since there are likely to be other Fred Blogs.
Having 2 pieces of information e.g name :- Fred Blogs, Mobile Number 0123456789, is personal because there is only one Fred Blogs from that number.
You don't always need the name.
A description such as:- The man who live in the High street, has grey hair, drives a green Ford Mondeo, walks his poodle every Saturday morning.
Could be classed as personal since it indentifies an individual, There is the assumption that the description is sufficient enough to prove that only one person who has these characteristics.
Of course the interesting things are email addresses. These are always unique, even if you work in a large corporation where there are bound to be multiple John Smiths etc, everyone of them will have unique email address. Since most sites where you have to register will ask for you email address at some point, this is personal information so the IP address is somewhat irrelevent.
Since mutiple home users will use the same PC or corporate users will be behind a single NAT address, an IP address itself could not be classified as personal information.