If by phone list you mean an itemised list of your bill (texts, calls, data), then yes, you can view your phone list online. How you do this depends on which network you're under contract with, but it's a really simply process most of the time.
How to view your phone list online
Most UK network providers now allow you to view a list of your calls, texts, data, and other phone services online. This cuts down the cost of "paper billing", and is also better for the environment.
Another bonus of online itemised billing is that it's quick to access, and you can usually track the bills back throughout your entire contract.
To view your itemised bill, go to your network provider's website and look for the "my account" button. Sometimes this might be listed as "Log in" or something similar, and is usually located in the top right corner of your screen.
If you've not logged in before, you may need to register, but it shouldn't take long. Once you're set up and logged in, click on your account and you should find the option to view your bill. If you click on this you will likely be shown a list of your latest months bill, and it will show you who you've text and called, and also any other data services you've used. Simple!
Here's an example of a Vodafone online itemised bill. Yours should look something like this:
