Second Undergraduate Degrees in Law at Oxbridge

Hello,

I am a senior (4th year student) concentrating in Social Studies at Harvard College, and will be applying for a second undergraduate degree with senior status at Oxford or(/and?) Cambridge, along with a few other schools in London.

Information online suggests it is possible to apply to both Oxford and Cambridge for a second undergraduate degree, but the link on the UCAS website which is referred to on Wikipedia et cetera seems to be broken. Would you happen to know whether this is possible, or would I learn about that when/if the UCAS application does not go through (i.e. is there a technical impediment to doing that)?

Also, if there is anyone out there who has applied for a second undergraduate degree in law from a US college, how has your experience been?

Finally, apparently one cannot make an open application for a second undergraduate degree; would that mean that the application does not get put in the larger pool for other colleges to consider if the applicant ends up not getting an offer from the individual college one applies to?

Thank you in advance, and best regards,