I'm not sure there has ever been a period in the USA's independent history when English universities were the first choice destinations for children of the elite to gain their first degree. As a rough proxy for "the elite", we can look at where the sons of US presidents have studied for their undergraduate education (I've included daughters in recent decades, since colleges have become more gender-equal). You'll see that not a single one has attended university in England for a first degree.

• Washington: his adopted son George Washington Parke Custis attended the College of New Jersey (now Princeton)
• John Adams: two of his sons attended Leiden University in the Netherlands (they were born in Europe), the third Harvard
• Jefferson: no legitimate son survived to adulthood
• Madison: no children; his stepson John Payne Todd did not attend university
• Monroe: no son survived to adulthood
• John Quincy Adams: three sons all attended Harvard
• Andrew Jackson: two adopted sons attended West Point
• van Buren: one son attended West Point, the other Yale
• William Harrison: his son John Scott Harrison studied medicine briefly, but I can't find out where
• Tyler: one son studied at Washington and Lee
• Polk: had no children
• Taylor: one son studied at Harvard
• Fillmore: son attended Harvard
• Pierce: no child survived to adulthood
• Buchanan: no children
• Lincoln: only one child survived to adulthood; he attended Harvard
• Andrew Johnson: had several children, but I can't find out where they were educated
• Grant: sons attended West Point, Harvard and Cornell
• Hayes: one son attended Cornell
• Garfield: three sons all attended Williams College
• Arthur: one son attended the College of New Jersey (later Princeton)
• Cleveland: one son attended Princeton
• Benjamin Harrison: son attended Pennsylvania Military Academy and Lafayette College
• McKinley: no sons
• Theodore Roosevelt: four sons all attended Harvard
• Taft: two sons both attended Yale
• Wilson: no sons
• Harding: no sons
• Coolidge: one son attended Amherst College
• Hoover: two sons both attended Stanford
• Franklin Roosevelt: two sons attended Harvard
• Truman: no sons
• Eisenhower: one son attended West Point
• Kennedy: one son survived to adulthood; he attended Brown
• Lyndon Johnson: no sons
• Nixon: children attended Boston College and Smith College
• Ford: children attended Wake Forest and Utah State
• Carter: children attended Georgia Tech and Memphis College of Art
• Reagan: children attended Arizona State, Yale, Marymount and Northwestern
• George H W Bush: children attended Yale, University of Texas, Tulane and Boston College
• Bill Clinton: daughter attended Stanford
• George W Bush: daughters attended Yale and University of Texas
• Obama: daughters not yet of age to go to college