If the lamp stays on with the bem connected there is either a short on the wire that brings the relay in or the relay is fused closed...

Cheers,
Tim

If I take the relay out and then turn on the key and put it back in I can hear and feel it clicking, plus have tried a relay from another car...

So I assume that means it's working and there is a wiring short then

So I got out the test light, and removed the relay. Tested each terminal where the relay would connect and found the following:

With key on
pins 85 & 87 have earth
pins 86 & 30 have +12V

With key off
pin 30 has +12V
pin 86 has nothing
pin 87 has earth
pin 85 appears to have pulsing earth test light flashes at me

you have tried a different relay, so if relay clicks in when you turn ignition on with BEM completely disconnected there is a short on the relay wiring between the BEM and the relay -(violet wire) - as Timmya says .......................

look for wiring jammed under a bolt (pedal box-handbrake steering column etc.) pierced with a screw or if someone has tapped off for alarm or cutout etc ............if you have wiring diagrams run new wire from bem to relay and disconnect old wire but there should be a reason for this problem....... seems both on line at same time does 85 flash when bem disconnected - does it have earth with test light connected to power (+ve)

So I had nice sunny weather today, figured I would crawl under the dash and see what was going on....

Surprise surprise - some muppet had made a right mess of the wiring. There were wires insulated with masking tape , wires that had been spliced and left un-insulated, and a wiring loom jammed under the sharp end of a rusty screw...

After sorting that mess out, I tried again, and still no go - however this time, unplugging the BEM turned the demister off! So out with the BEM from a donor car, into the EB, and hey presto! It all works now!

Thank you to everyone who has helped me solve this, and a huge thanks especially to TedW and TimmyA - you guys are legends!

good to hear,puts a smile on your dial doesn't it .

sounds like the wiring guru had shorted the bem out