Can't email from apps, despite working email

I can't email from Safari and other non default apps despite having a working email.

Details:

My email settings are just fine. I can email and receive mail.

But trying to share a link, for example from Safari via email, I get a new window and I fill in the 'To:' field, finish the email and it appears to be sent. As in, I get the 'swoosh' sound. But then the email never arrives.

This doesn't only happen from Safari, but other apps too like Tweetbot and Week Cal.

Is there a way to debug/fix this behaviour as it only started to happen in the last week?

Thanks for your time