“View post” leads to odd URL

On one of my sites, pressing “View post” from the back-end creates an odd URL, always taking the user to the homepage.

The correct URL shows when you mouse-over the link – for example –

But when clicked it leads to:

This happens when all the plug-ins are deactivated and with any theme I switch to.

Googling for an explanation is a dead loss. Has anyone experienced this before, or can anyone suggest what is happening? Something in wp-config or htaccess? Many thanks.