No, that would be ridiculous. Just because you meet the requirements doesn't mean you'll definitely get an offer. Oxford, UCL and Bristol, and to some extent Warwick, are immensely competitive and therefore are all high risk options. Presume you get an offer from Oxford, or any of those Universities par UCL, you don't actually have an insurance which isn't the brightest of ideas.
In short, I wouldn't add another option based on entry requirements.
In terms of the LNAT, quite simply it depends on how good you are at exams under pressure and critical thinking. If you're excellent at both, then it shouldn't matter.