In Search of Your British and Irish Roots by Angus Baxter, 1982,  refers to the custom in England and Wales from 1700 - 1875. This custom was also prevalent in Colonial America and provides valuable clues to ancestry.

1.  The first son was named after the father's father

2.  The second son after the mother's father

3.  The third son after the father

4.  The fourth son after the father's eldest brother

5.  The first daughter after the mother's mother

6.  The second daughter after the father's mother

7.  The third daughter after the mother

8.  The fourth daughter after the mother's eldest sister

There were exceptions - if the eldest son was named "John" after the father's father, and the mother's father was also named "John", the second son was named after the father.

Hardly anyone had middle names before 1731, when they began to increase slowly. By 1783 they had become more fashionable, though not nearly as common as at present.