Drivers who break the laws of the road can expect to be fined and have penalty points added to their driving licence (if they have one yet).
It is also fairly certain that any potential or existing insurance provider is going to look closely at the conviction on the licence before offering any insurance premium. Remember, fail to disclose a conviction on your licence and you could invalidate your insurance policy, whereupon you could find yourself driving around without insurance thereby committing a further offence.
In the event of being caught speeding at say 39 mph in a 30 mph area, one would attract 3-6 points penalty on a licence together with a fine of around £40 - £60 usually, depending whether it is the first offence.
Get caught speeding and not being licensed to drive, failing to have either the minimum insurance requirements or a valid MOT at the same time, and it can be treated differently.
In situations where a person committed more than one offence at the same time, such as speeding and not having a valid licence to drive, courts usually convict on the most serious offence. In the case of our speeding driver who did not possess a driving licence, it is also likely they therefore did not have any insurance either.
Driving without insurance usually attracts 6-8 points penalty and by far the most serious offence in this instance. The person should also expect a fine of a few hundred pounds.
In Devon for example, a man has just been jailed for 6 months for driving at over 120mph on his motorcycle with his son as a pillion passenger. He has also received a 6 month driving ban so the conviction and additional penalties can vary in exceptional circumstances.
For individuals convicted of driving without a licence, the penalty will be stored by DVLA and added to their licence when they apply for one, so there is no escape once convicted.