He did say it would be £100 fine and three points but assumed as it was dealt with there and then I would have heard within a few weeks?
I would have expected to receive a COFP - Conditional Offer of A Fixed Penalty - for that. There is no legal time limit for these. Basically it says "plead guilty now and accept the 3 pts and £100 fine and that'll be the end of it". However, before one of these can be issued, they have to check that you aren't already on 9 points, plus a few other things. So the rozzer takes down all the details, gets back to the station and then passes the paperwork onto a decision maker. If you are issued a COFP, then you normally have 28 days to respond to it, either accepting, declining or ignoring their most gracious offer.
Should you wish to ignore , decline or dispute their most gracious offer, then after the 28 days have expired they will (should!) assemble the 'information' and file the charges before the magistrates court. That may take a few days to sort out, depending how busy the busies are. This DOES have a time limit - the information must be laid before the courts no later than 6 months after the date of the offence. Once that happens, the courts will eventually (a few weeks later) send you a summons to appear before the magistrates and explain why you are messing them about by pleading not guilty. They then find you guilty regardless, put on the black cap and sentence you to death.
So - getting a COFP within 28 days of the 6 month limit is effectively a get out of jail free card. If you do not reply to it, once the 28 days have elapsed it's too late for charges to be filed with the court. However, there is no requirement for them to issue a COFP, so they could go straight to summons in which case you won't be 'safe' till Feb 18th, and you won't know you are safe until early March.
IMHO, if you get a COFP now you are home and safe. However, you've got to sweat on a summons landing on the doormat for another 6 weeks or so. Whatever you do, don't rattle the cage - you don't want them looking down the back of the filing cabinate, or hunting through piles of paperwork to find your file and working out what has happened. Stum!