I assume the white thing you are referring to is the electrode, which is where the spark is emitted.
If the electrode has been replaced, its worth checking the wiring.
To rule out the spark generator, I would switch over the cables to use a different terminal and check it sparks, if it does then you need to check if the terminals are loose, and potentially replace the spark generator. If there is still no spark when you swap over the electrode cables the fault will be due to the burner not having sufficient earthing for the spark to ground itself, so I would look to clean the burner.
As this is a gas appliance I suggest you use a gas safe engineer to perform these tests.
Please let me know if you need anything clarified.
The engineers in your area are rather expensive, I imagine due to the being in the South East.
Your looking at around £80-83 to have someone come out in labour charges alone.
If your happy its not the burner, then its likely to the spark generator which can be sourced from here for around £42.
Based on labour and parts costs your approaching the cost of a new hob, if you would like to proceed I would recommend you use BHL, who can be contacted on 01842 879585.
Please let me know if I can be of any further assistance.
I havent heard back from you in the last day or so, and just wanted to check if you still require assistance, I would appreciate it if you could rate the service received.