This post from 2006 puts it down to heating:
My laptop toshiba shut down by itself
or
Help! Toshiba laptop shuts down by itself (crashes) - TechSpot OpenBoards but this one does suggest that BSOD is possibly not heat related.
The majority of the posts are indeed heat related.
There is one other cause - the name begins with T
As Milo says it seems to be a generic fault and the number of posts on the web support that. The solution (or fix) lies with the supplier not the manufacturer.
Problem with getting another replacement is the software and data hassle. Perhaps get an external HDD and copy all your files across then go and hit Tesco for a refund.
If you can make the problem predictable and repeatable then you should have no problems and no fault found when they reformat your machine and 'soak test it' for 5 minutes.