When I adopted Merlin, I was told he was not chipped. The vet fortunately scanned him, before sticking the needle in, and discovered he was already chipped. They gave me his tag number, and I contacted the microchip company. I gave them an account of when, where, who, I got him from, and they contacted the registered owner. She never replied, so after 6 weeks, they simply transferred ownership to me.
In the UK, a dog can be 'stolen' however a cat cannot - They are considered wild, and therefore cannot be 'owned' as such to become a material possession. If you have been paying - and can prove you have - all the vet bills, etc., then it is extremely unlikely police would be involved in a cat being returned to somebody simply because they suddenly say (after a prolonged period) that yes, they want the cat.... This would end up a civil matter in court.
Don't worry - just get the paperwork done and push them to transfer the records to you as soon as they can!