king's is the infamous one that has a 30+ cutoff, and is pretty straight-up about it. all other universities deny having one (however truthful you take that to be) and look at the lnat holistically with the rest of your application. glasgow typically allows slightly lower lnat scores through if the rest of the application is top-tier. on the other hand, places like ucl, durham and lse probably do have a score beneath consideration simply because of the sheer number of applications they get with grades like A*A*A*.
i know someone who got 29 on their lnat score and got rejected from ucl on the grounds of a "low lnat score", but someone else i know that got 28 got in. so no, if they say there is no concrete cutoff score, then the best you can do is take their word for it.