I am not familiar with the UK, but even in the US it varies from state to state.
People who aren't explicitly protected by state law get fired for putting something on the internet that their employer doesn't like. There is an explicit carve out in California law (http://www.leginfo.ca.gov/cgi-bin/displaycode?section=lab&gr...) I don't know if there are any other states that have this carve out, but that section combined with "Section 16600 of the California Business and Professions Code states that "every contract by which anyone is restrained from engaging in a lawful profession, trade, or business of any kind is to that extent void." makes quitting your job, taking your own IP made on your own time, and competing with your employer. A protected activity. in California.
Some will tell you otherwise (Google does this) but I sought out advice from a labor law attorney on the legality of their claim and his opinion was that it was largely unenforceable. You couldn't use proprietary information in your gizmo but you could, for example, write a phone operating system on your own time and equipment, quit Google and start competing with Android and they would have a hard time preventing it. But only in California, the employment agreement would hold up in Boston for example.