Did your client get a bounce message when trying to reply to the email from you?
Check your Deleted and Junk mail folders. Are the missing emails in there?
Missing email isn't a typical warning sign for hacked accounts but it's always possible someone else has access to your account too. It can't hurt to change both your password and your security question & answer.
The mail servers for bbc.co.uk do not appear to be on any blacklists.
Are you getting any email? Are you missing some or all of your incoming email?