You're becoming paranoid!
Nobody has broken in. Nobody is piggybacking off your internet connection. The settings within any electronic devices can be corrupted by power surges (such as millions of household experienced during the recent storms) or even by solar radiation. That will, almost certainly, be what's happened in your case.
Since you know how to access your router's settings, go into them and look for an option to go back to your original settings. (If you're really sure that you know what you're doing, reset the router to its factory settings and then enter the required information manually:
http://community.talktalk.co.uk/t5/Community-Help-Articles-beta/Setting-up-a-Non-TalkTalk-Router/ta-p/1324129 )
However, if you're only getting 0.3Mbps then it's still most likely to be a line fault.