Thanks for th plug Lewis!
Mr Underworld, the Supra doesn't have an immobiliser built in as standard. There is definitely nothing in the key.
The alarm you have, does it immobilise the car itself? - In theory, if you were to get out of the car and leave it for a few minutes, it should immobilise itself. If it does, it could well be a Thatcham approved model. If it doesn't, it won't be insurance approved. (with the exception of the shite Scorpion thing fitted as a dealer fit to UK cars).
If you want to have a day out to Maidstone, I'm more than happy give it a look over and if it is, I can do you a certificate for it.
Do you know what make it is?