While driving car shakes then stability control light turns on

It does sounds like the car is misfiring which can turn the warning lights on. To be sure we should run the codes. here are two guides that can help us fix it:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

and

https://www.2carpros.com/articles/engine-misfires-or-runs-rough

Please run down these guides and report back. Can you please shoot a quick video with your phone so we can see what's going on? that would be great. You can upload it here with your response.

That's what happens when I turn it on or I park up. not sure what else you would like to know i a emulsions warning light and stability control one when it starts to judder. thanks

thanks for the video. Lets remove the spark plugs and do a compression test. these guides will help us:

https://www.2carpros.com/articles/how-to-change-spark-plugs

and

https://www.2carpros.com/articles/how-to-test-engine-compression

keep the plugs in order and send pics of the electrodes.