Okaaaaaayyy.....Bulgin light screens, we're well and truly in my arena here (I run a 16 ft light-show and I've had the shocks to prove it).
They're simple enough to fault find on so long as you're fairly savvy with electric....and bear in mind these will be running at the full 240v. Bear in mind as well that they can also be a fire hazard if you get it wrong (I've got some of the partitions in my screens which were charcoal when I took them over).
Firstly, I doubt the PAT stickers are worth the paper they're written on. I know from the PAT testers I've used they'll happily test the controller, but won't test the boxes (the "official" test so I'm told for the Bulgins is to run your finger around it and see if you can touch the contacts....not recommended).
First question - how many boxes/physical lamps are you connecting in the chain and what wattage are the lamps inside? There's a limit on the total current draw you can output per channel on the controller, and obviously a total draw across all channels.
What happens if you only plug a single screen in? Does it blow then?
As someone else has said, it could very easily be a loose wire or a short circuit as well. You'll normally find anything like that in the back of the lamp holders themselves (bear in mind they get shook around during transportation, they get hot in use....). Whenever I take on a "new" light screen the first thing I always do is re-wire it, mainly for my own piece of mind, but I've also found them with badly perished wire or even the wrong grade of wire inside in the past (most of these things are home made).
It could also be the condition of the Bulgin plugs/leads themselves (are they homemade or professionally made?)
Hopefully there's a few pointers for you, but if you need any more help, please shout.
Disclaimer - I'm not a qualified electrician, but have gained a lot of experience in the workings of these things. If you're in ANY doubt as to what you're doing....contact a qualified electrician rather than risking electrocution or fire!