Yes they are interested in all convictions and fixed penalties including those for minor motoring offences. From the guidance notes:
“You must disclose any convictions, however minor, including motoring offences where either a fixed penalty was payable and penalty points endorsed on your licence, or for which you attended a speed awareness course. You must also disclose any criminal or civil orders to which you are or have been subject, including details of divorce and maintenance orders, as well as penalty notices for disorder, warnings for possession of cannabis, Anti Social Behaviour Orders, all forms of formal recorded caution.“
I believe you can get a form from your local nick to apply to be given details of all information held against your name on the Police National Computer. You have to provide proof of identity and pay a fee (£10 I think).