Thanks. It is Outlook 365 I am experiencing the problems with (but did have the same with Outlook 2010 earlier). I have reinstalled and done all I know but the problem persists. The internet connection is fine; it is not "Offline"; and the Hotmail web emails work fine. I have removed the emails and all works well so long as I never look in the Outbox at any emails there. I f I do that, the emails change from italicised to non-italicised and will not send.
It is a Hotmail account that uses the MS Exchange ActiveSync.