Just to add a bit of flesh to the bones:
Point 1. If you were stopped at the time of the alleged offence (rather than being detected by a remote device) there is no obligation for you to receive a Notice of Intended Prosecution (NIP) at all. The police officer stopping you will (if they do their job correctly) warn you that you may be prosecuted. If you are not stopped at the time, as has been mentioned, a NIP must be sent so that in normal circumstances it should arrive with the registered keeper within 14 days of the alleged offence (with the day following the alleged offence counting as day 1). Failure for the notice to arrive does not necessarily invalidate further action though the prosecuting authority may have to show a court that they had sent the notice so that it would normally arrive in time. In either case the prosecuting authority has six months to “lay an information” before the Magistrates’ Court. This is an absolute time limit and there are no exceptions to this.
Point 2. If you send too much cash in response to the offer of a Fixed Penalty the Fixed Penalty Office (FPO) has the option to withdraw the offer and instead begin court proceedings (which they have six months to do, as above). They have the option to do this if you fail to comply with any of the conditions of the Fixed Penalty offer. The offer is a concession which is made to drivers who wish to accept guilt and avoid going to court. It is not a right and can be withdrawn. Usually they will write to you first asking you to submit the correct amount, though some FPOs may operate differently. None of this prevents the addition of points to your licence. If they were solely interested in getting cash from you they would not offer fixed penalties at all. Drivers who are sentenced in court for speeding are fined at least half a week’s net income plus prosecution costs (usually about £85) and a Victim Surcharge (now 10% of the fine with a minimum of £20). All this adds up to far more than £60.
Hope this helps to dispel some of the "urban myths".