Matter in what context? Job prospects are going to be similar between them (and still largely dependent on you and what relevant work experience, vacation schemes etc you have picked up during your degree). Academically they are roughly on par although one may be better than another in some particular area, and the teaching format at Oxford is unique among the three.
Another factor to consider are that at LSE and UCL are both in London and thus would entail living in London and all its costs. There's a good chance you will be spending a huge amount on rent and transport while living in a shoebox 45 minutes commute away from the uni after first year! However both also may permit you to take "outside modules" in other subjects than law, which you can't at Oxford typically I gather.