If you have one speeding conviction it probably will not make a huge difference to your insurance premium as most insurers recognise that its very easy to collect a few points from speeding these days.
However, for more than one speeding conviction it may start to have an impact on your insurance. Many insurers believe that the number of speeding convictions has a relationship with the likelihood you are to make a claim. If you have convictions on your licence for speeding or any other offence it could be worthwhile in comparing quotes from insurers who specialise in providing convicted driver insurance.
Insurers generally want to know about any convictions you have in the last 5 years and these will be used to help them calculate your premium. Drivers with speeding convictions have increased massively over recent years largely due to the automated tickets issued by speed cameras.
It is now pretty easy to pick up a speeding conviction a regular driver may pick up more than one set of points for speeding.