About 75% of British lawyers (including both barristers and solicitors) attended what we in the U.S. would call private schools rather than what we in the U.S. would call public schools (compared to 7% of the British population at large, which is less than the comparable U.S. figure). Their families also had incomes 64% higher than the average (the difference, for example, between $50,000 and $82,000).
While this isn't a surprise, the extent of this gap is more than the current government there is comfortable with. I'm sure that the percentage of U.S. lawyers who attended private schools far exceeds the percentage in the general public, and that lawyers grew up, on average in households of above average income.
My intuition is that there would be less of an education discrepency (at Ivy League law schools maybe, but there are something like 180 law schools in the U.S., many not so blue blooded) and more of an income discrepency (the income disparity is probably greater than that at most colleges and universities, public and private, that send large number of students to further education). But, it has been some time since I've seen hard numbers addressing similar issues (e.g. selective college attendance statistics) and I don't have them close at hand.