Many thanks for the reply Roy. Maybe I didn't explain the problem fully - yes these both happen at the same time with both the ignition on, and engine running, and with no switches operated. Yet it only happens when the interior of the car is cold (it was minus 6 when I collected the car from Amsterdam - and it is a LHD). Once the interior warms up the problem ceases, I drove it over 800 km continuously with no problems at all just after I bought it, then it happened again the following morning in the UK, so I sensed it was something to do with a short, or condensation caused by the cold/damp conditions. Your diagnosis of it being the BII (what exactly does this stand for???) seems spot on. I havn't had chance to check for any water leak, the car went straight in for a service with a Merc trained technician, but I'm not sure he would suss this problem out. I look forward to your reply and again, thank you.
I was a Renault RTE and worked on these vehicles at a main dealer and like most modern cars they are fairly complex electronically. The BII is the internal main computer that controls many of the cars functions and liaises with other computers via high speed multiplex wiring. As your car is LHD it should be under the floor on the right hand side which is your passenger side. These vehicles have an independent cabin heater that operates when the outside temperature is very low (less than 5 degrees IIRC) and the engine coolant is below 85 degrees and since your problem only occurs when cold this might be involved in some way (crossed circuits) but it still suggests some wiring or computer fault. I was also a Merc technician before working for Renault and I can tell you that I would not have understood the Renault as they are so different and their diagnostic equipment is also much different. So unless they have changed since I was there, I'm afraid you need to get it checked by a Renault dealer to see what fault codes are coming up. As it needs to be cold, you would need to leave it overnight so they could experience the problem and check it while cold.
I have never come across this before, but if you do take it to a Renault dealer, ask to speak to their RTE to explain the problem directly - not through anyone else where the facts may get changed/distorted or be simply incorrect. We always tried to speak directly with customers and that was part of the function of the RTE.
Roy