If by primary cat you mean the small catalyst nearest to the engine; this may be sufficient to pass the MOT 'emissions check', but it is woefully inadequate to meet the UK emissions regulations. It's only there because it's small, close to the engine and warms up more quickly than the main (secondary) catalyst, so becoming active sooner. Often it is only an oxidation catalyst to take out initial cold start HC and CO. Does nothing for NOx emissions.
Without the main catalyst, the tailpipe emissions out on the road will effectively be at the same level as engine-out, i.e. NOx will be more than 10x higher than the regulated limit.
There is a lot of discussion about the effects of vehicle exhaust emissions on local air quality. Removing the secondary cats should be illegal IMHO.