Ah, I see what the issue is. You added a logo on the Site Title element via custom CSS:
.site-title a {
background: transparent url("https://swimquest.uk.com/wp-content/uploads/2015/11/SWIMQUEST_LOGO_FOR-WEB-e1448796620370.jpg") no-repeat scroll 0 0;
display: block;
height: 80px;
overflow: hidden;
text-indent: 100%;
width: 305px;
}
So if you now hide the element either with custom CSS or via the Customizer, you end up hiding the logo as well.
The text-indent: 100%;
part of the above code should in theory have been hiding your site title text, but I think something the CSS isn’t quite right.
Try replacing the entire block of CSS above with this instead:
.site-title a {
background: transparent url("https://swimquest.uk.com/wp-content/uploads/2015/11/SWIMQUEST_LOGO_FOR-WEB-e1448796620370.jpg") no-repeat scroll 0 0;
display: block;
width: 305px;
height: 75px;
text-indent: 100%;
white-space: nowrap;
overflow: hidden;
}
Now add back your site title – let me know how it goes.