UK law on wiring up your own house with CAT-5?

This gets very hard to say and in the US it even depends on the city.

There are certain standards that you must follow to meet the electrical codes that vary a little from country to country. Low voltage stuff has the least restrictions allowing things like cable splices in walls without boxes. Meeting the standard is actually the easy part.

The problem comes who can do the work this is not part of the national codes it is unique to cities.

In many cases there is a exception that allows the owner of a residential building ie house to do any electrical work themselves. Even in commercial buildings many times there are exceptions for low voltage cable that allows a non electrician to run them.

The next problem is if you need a permit. This is mostly a money grab by the city. They many times even after you pay the permit fee will refuse to come out and inspect the work...and that inspection is what the fee is suppose to be for.

Most the cities you have huge problems with have a large union population. There was a case in a Massachusetts city that said a painter could not remove the plastic front plates on a outlet box. you had to pay a electrician to come in and remove them and pay them again to reinstall them.

The best bet is to do the work correctly but tell no one. First few cites keep good enough records to know what you had permission to install and what you did not.
Mostly the risk is if you go to sell the property and you did not do the work correctly the inspector hired by the buyer will make you correct the work and this time you will be forced to use a licensed electrician.