Do you work in a small business with a fairly amateur approach to IT systems? If your colleague can use your email address then so can the cleaner, or the cleaner's stand-in.
I think it's an issue for the management of the business to understand that lax security could become a business issue, if for example, someone sent illegal porn from one of their addresses, which could result in a police investigation and seizure of the computers and servers.
Rather than having a row with the lady, take it up with the management, and point out the benefits of security.
Such security is easily available using Windows XP Pro, which has password security for individual accounts on one PC. It's basic stuff that could be set up in minutes by a user with the manual.