'ello mate!
I've got a similar problem with work emails at home, except I can receive but not send. Our problem is due to the fact that our website & email addresses are held on our web hosts server which has problems with getting too many email requests (apologies if this isn't the right techy talk, I don't know too much about this!) and basically spits its dummy out. Don't know if this is the same thing with you mate but it could well be??
Apparently the fix is getting a proper server in the office and then I don't know what, as this is about as far as I get before switching off when our IT guy starts