Thank you lazydog. Yes, I do want to shut it down so they have to call me or at least make contact before going on. Will have a look at what you've mentioned first though and it may give me the security I want. Thanks again.
If you don't simply want to shut it down entirely (which would mean they'd have to call you first, to re-start logmein before they can connect, and may be what you want?) have a look at page 28 of this user guide: https://secure.logmein.com/welcome/documentation/EN/pdf/Free/LogMeIn_Free_UserGuide.pdf
You need to go to Options > Preferences > General and then under "Host-side user's consent" make sure that a remote connection requires consent. Also ensure that the option to refuse connection if the timeout period for a response has expired, is set.
Our computer engineer has left logmein set so that it automatically starts when the computer is turned on. I'm not happy with that, so would like to disable it so that a request to access the computer remotely has to be made. How do I do this please?