Newb99 is correct on this issue, It is NOT illegal to use a computer/device in a UK casino as long as the device does not interfere or alter the outcome of the game. For example. magnets on a roulette wheel would be illegal, whereas a roulette computer predicting where the ball will land would not.
Moo123 - US laws have absolutely nothing to do with UK laws, what happens in Nevada may as well happen on the Moon.
SuperTrump, yes you could legally use the device pictured, however it only keeps a running count. If you going to go to the trouble of using a computer, risk getting thrown out, chips/money confiscated, Police hassle (believe me, they would still be called incase you were up to illegal activities) legal battles and whatever else the casino try to throw at you, then you may as well use a decent computer and pull a large advantage. I hear there's a company in London that manufactures good quality roulette prediction computers that look like mobile phones for a few thousand quid each, they are supposed to be very good. However, you need to master ball measurements, so you also need to buy a casino grade roulette wheel so you can practise. You'll also need to be able to place many neighbouring bets very quickly, so you'll also need to be a master with both table and wheel number locations. Sorry can't help with BJ computers but I would imagine that anybody offering to sell "casino beating computers/devices" is 99 times out of 100 either a con artist or selling a worthless product (as you pictured).