This is an excellent and sophisticated question. There would be many, many ways to think about this, such as conservation of energy, material science (you can not just slim down materials abstractly, issues of tensile strength, laminar flow etc, become critical), farming and food production, and so on.
Just one interesting issue which would need to be examined is the extremely highly variable ratio of cat groundspace in different postures, compared to humans who are generally upright except when sleeping.
Comparing cat to human as such is simply misguided.
The best calculation would be to compare the size of a typical cat house to a typical human house.
If you think of quaint London terrace houses, I just googled the typical width of the street frontage is about 6 meters.
Now, picture an imaginary cat house, such as in the film The Cat Returns where our heroine shrinks down to a world of cute little cat-size houses,
Compare house sizes.
Cat fanciers will be able to answer the question, about how wide would a cute little cat-house be?
Let's say one meter across.
(It could be more like 1.5 .. I don't know. The worldbuilder, or some cat fanciers, would decide this.)
Let's use a calculator to divide 6 by 1, it turns out
Cat Britain would be 1/6th the size of actual Britain
In fact, Britain is conveniently 1000 km long and 500 km across.
So the actual answer to the question is
Cat Britain is 160km long and 80 km across.
So that's it.
Note that issues of volume, weight etc are totally irrelevant.
UKCat would have cat-cars, cat-skyscrapers, cat-trains, cat-roads, cat-Tescos, cat-Brexit and so on.
You simply have to decide on how wide a cat-terrace-house would be compared to a normal-terrace-house - I've said "one sixth" - and you have your answer.