Not quite.*
There is no law that says you must run cats, and as such there's no law stopping you from running decats. However, under the C&U Regs 1986 S61 Linky:
...or in plain English, if you make your car produce worse emissions than as it comes out of the factory you can be prosecuted, so this also applies to hi-flow cats as well. The EU Regs mentioned refer directly to the emissions of the vehicle, which is why the statute simply puts those rather than actually give us the detail. It's exactly this kind of stuff that's going to be a nightmare to de-tangle from when we Brexit, so now you can see why it's going to be many, many years before we take back control etc. Interestingly the text reads "or permit to be used", so if you let your missus drive your car with hi-flow cats on then you can both be charged.
However, back in the real world this is never ever ever going to happen. Ever. If you get stopped and charged under this precise law, I'll pay the fine for you. Realistically if you've got no cats then your car will be antisocially loud (for the most part), so they'll simply S59 you instead which requires no proof and has no right of appeal. Far less paperwork than calling the DVSA (VOSA) out to actually carry out a proper test on the vehicle, which would be required for conviction as otherwise it's not beyond reasonable doubt, and unless you strike really unlucky and happen to get stopped on a random DVSA test (again super unlikely as they go after commercial vehicles 99.9% of the time) it's not going to happen. With fewer resources these days it's even LESS likely to ever happen.
In short: Fit and forget, just don't drive like a knob. But that applies all the time anyway.
*These laws are for England & Wales, I would imagine there's not much difference in Scotland but alas that's more difficult to find. Happy to be corrected if you can show me the proof.