There’s two categories of Oxbridge.
There is the group that did undergrad law in Oxbridge. They have a special group and they are generally quite close and well connected.

There is another group, the FCH in NUS who go on to do BCL or LLM at Oxbridge for the sole purpose of becoming an academic (Asst prof from Sheridan fellowship) or just the prestige required for top litigation sets. Most barristers in tier 1 chambers have the BCL/LLM from Oxbridge.

The second group would not be as connected as the first group, but they do have the connections from their BCL/LLM