Hi, thanks for your reply and sorry for the delay coming back to you (I have been abroad).
I did change the tagline field as suggested but nothing changed on the actual page. Also, in the custom options itself, there are options for having: header, text (no header), or disable (i.e. remove both). But not, it seems, an option to show your custom header AND the tagline at the same time.
For now I've added the contact info in the slogan field but this isn't super ideal as I can't add HTML to the email address (have tried, but it get stripped) and it also shows the slogan on the blog page. Not the end of the world, but not ideal.
I'm moving in the direction of physically adding the contact details to the bottom of the logo (as part of the image). Not perfect (as they won't be clickable) but may be the best way (unless any one else has a better idea).
The only other thing I thought, would it be possible to replace (or restyle?) the search box (which sits top right and which I currently have hidden) with contact details? Not sure.