If you get points then you have to inform your insurance company once you have the points - not telling them until you renew your policy could well still invalidate your insurance - it comes under the bit where you agree to tell them of any changes in circumstances. So whether it is points/modifications to your car etc, if you don't notify them and then try to claim on your insurance you risk them invalidating it meaning your insurance is totally worthless.
Equally, when you renew your policy/get quotes from anywhere else you need to tell them, yes it will make it more expensive - but still a damn sight cheaper than being found having no valid insurance would be! Insurance companies will increase your premium - the amount will vary depending on what the points are for, how old you are, how long you have been driving. But it can be a substantial amount, or can be fairly small, depending on those factors. Points are valid in terms of adding up to disqualification etc for 3 years, but they appear on your licence for 5 years and most insurance companies will ask if you have any points within 5 years.
If you get the option of a speed awareness course then you don't have points on your licence and therefore the insurance company won't increase your premium. I've been on one of these courses recently and was told whilst there that we should have informed our insurance company that we have a NIP for speeding, which was pending, as until we have successfully been on/taken part in the course the insurance company should be informed, so again, could try and invalidate insurance. In reality, since none of the paperwork I had been sent said this on it, I would argue that it wasn't explained that we needed to do this - whether than would have worked if there had been a problem, I don't know!