I would suggest you make your application for ILR now. I appreciate you have an unspent speeding conviction, however, the UKBA will normally disregard a single conviction for a minor offence resulting in a bind over, conditional discharge or relatively small fine or compensation order, if a person is suitable for grant of leave in all other respects. By 'minor offences' it means speeding or other 'regulatory' offences.
Offences involving dishonesty (for example theft), violence or sexual offences are not classed as minor offences. Drink-driving offences, driving while uninsured or disqualified are also not minor offences.
Thus, if you were found guilty of speeding, this would constitute a minor offence.
In any event, if your application for ILR is refused, you would then have sufficient time in which to apply for Further Leave to Remain if you had to.
If you wish to discuss, please feel free to ask further questions.
I would suggest you make the application under the 5 year routs as the application should not take as long to process as it does for the 10 year long residence route.
And yes, they do apply some discretion to 'minor offences', of which speeding is deemed as a minor offence.
If it makes you feel better, I suggest you have a immigration lawyer prepare your application for you.
DISCLAIMER: Answers from Experts on JustAnswer are not substitutes for the advice of an attorney. JustAnswer is a public forum and questions and responses are not private or confidential or protected by the attorney-client privilege. The Expert above is not your attorney, and the response above is not legal advice. You should not read this response to propose specific action or address specific circumstances, but only to give you a sense of general principles of law that might affect the situation you describe. Application of these general principles to particular circumstances must be done by a lawyer who has spoken with you in confidence, learned all relevant information, and explored various options. Before acting on these general principles, you should hire a lawyer licensed to practice law in the jurisdiction to which your question pertains.
The responses above are from individual Experts, not JustAnswer. The site and services are provided “as is”. To view the verified credential of an Expert, click on the “Verified” symbol in the Expert’s profile. This site is not for emergency questions which should be directed immediately by telephone or in-person to qualified professionals. Please carefully read the Terms of Service (last updated February 8, 2012).