Is it illegal in the UK to post styling that breaks out of a post?
For instance, if styling were allowed here and I were to use it to change some stackexchange pictures on this page, would that be illegal?
In the UK, the Computer Misuse Act of 1990 does make this illegal if you do anything on the server:
Section 1 of the act makes unauthorised access to computer material a criminal act, punishable by 6 months' imprisonment or a fine "not exceeding level 5 on the standard scale" (currently £5000)
This is a very wide-reaching act, and is a major reason for some of the disclaimers security testing companies require, as it doesn't even require you to change anything - simply accessing the computer system or data can be enough.
If you are simply doing it on your own computer, replacing images or content as you see it, you should have no problems.