I will rely on two sources and two dates to provide the information asked in the title. In this article the word “neutered” means both neutered (male) and spayed (female).
As at 2012, the RSPCA state that neutering rates of owned cats stood at 86%. The PDSA in their report state that 90% of cat owners have had their cats neutered as at 2017.
The PDSA also state, however, that 13% of owners of a female cat say that their cat has had at least one litter.
The RSPCA also state that research tells us that in order to maintain a stable domestic cat population (i.e. not increasing) neutering rates need to be at 92%. In other words both figures of 86% and 90% are too little and it means that unwanted cats are still being created in the UK.
As at 2012, the RSPCA reported on a cat crisis as they describe it (too many unwanted cats causing problems of space at RSPCA shelters). They stated that although most cat owners are predisposed to the idea of neutering, twice as many people do not neuter their cats in the socio-economic groups C2DE compared to the group ABC1.
Also, acquiring a cat spontaneously is far more likely to result in the cat not being neutered. In the UK, there is also the one litter myth which is that some owners think that a female cat needs to have a litter before being spayed. This appears to become a “deeply ingrained social norm. The same problem exists in the USA as well.
The PDSA also report on the same problem which I have referred to above (the 13% figure). There are many schemes in the UK for discount spaying and neutering but clearly many people do not avail themselves of the services.
I hope this post answers the question in the title.