I was hoping it was a diesel and then I could have suggested glow-plugs.
It's 20 years now since I last owned a petrol car but "mucky plugs" was a favourite cause of lumpy running, as was the points. I suspect the diagnostic machine would have identified a faulty engine temperature sensor but engines have moved on so much since I last had problems that most of the things that gave problems back then have been made more robust so I can't think of any other suggestions offhand. Sorry.