Thank you Padgett.
"This is not for the amateur, you really need to know what you are doing"
When I said I'd tried to open the case, that wasn't strictly true. I'm a klutz and I'd have broken it. So, what I actually did was take it to one of the IT field support guys at the company I work for. They fix laptops all the time so I had more condidence in them doing it than me. Plus they had the right sized screwdrivers 
However even they couldn't prise the case apart.
But now, armed with your reply, I'll ask them to try again. And see if they have a crowbar too.