UPDATE:
I had an auto electrician come out to look at it, and he's told me I need to replace the ECU, as there is an intermittent fault meaning that the imobiliser is kicking in after deactivation, and that the ECU was being blocked.
Another fault that kept coming up after being cleared was 'speed sensor' something or other. He did tell me, but I've forgotten exactly what it is. He said he tried to get the code off the ECU for the imobiliser, but he said he couldn't because he didn't have the specialist equipment required.
Do I get a new ECU, transponder & key, or can this issue be sorted out some other [cheaper]way?