Oh, my God! I’ve just had one of those inverse Eureka moments. WordPress has the facility to display the permalink structure in a logical manner – i.e. so that it makes sense; date and name based, rather than a series of numbers. I’d set it to that. When I reinstalled WordPress, it defaulted back to the original setting. Fer cryin’ out loud… That’s why the friggin’ links didn’t work. 
Mrs Longrider was spot on…